Methods of presenting data.

Methods of presenting statistical dataThere are different methods of presenting data in statistics and Geography. Generally, tables and graphs are among the effective communication technique that interpret and convey statistical data and information. They enable readers to understand the content of Geographical statistics, sustain their interest, and effectively present huge quantities of information. Statistical graphsThis group is basically concerned with the relationship between quantities and does not stress the idea of location. Usually, the horizontal and vertical axis must appear as a basic and integral part of the drawing. These graphs are subdivided into

1. line graphs
2. bar graphs
3. age and sex pyramids
4. dispersion graph or circular graphs.

Line graphsLine graphs may be represented in four (4) ways:

1. Simple line graph
2. group line graph
3. compound line graph
4. divergence line graph.

Procedures for drawing line graphs

1. The horizontal axis is normally used to represent the independent variable, for example time whether in hours, day, month’s years or any other period of time;
2. The vertical axis is normally used to represent the dependent variable for example quantities or values, sometimes as percentages;
3. Select the suitable scale by considering the highest value in the graph space; If drawn on plain paper, it is preferable to draw two vertical axes, one at each end of the horizontal axis;
4. Do not indicate large numbers with long strings of roughs, for example 100 000 or 200 000 but write either at the top corner or along the side, the value of the units expressed in figures. For example tonnes;
5. There must be a title, a scale and a key.

Note: The procedures above are stated in general way however, they may slightly vary depending on the type of line graph dealt with. Simple line graphThe simple line graphs are normally drawn to represent the time series data related to the temperature, rainfall, population growth, birth rates and death rates. They are called simple because they have a single line. They are commonly used in hospitals as well as meteorological and dermatological stations. Procedures for drawing a simple line graph

1. Identify the types of variables from your given data to horizontal scale (independent) and another in vertical scale (dependent);
2. Select the suitable scale by considering the highest value and the graph space;
3. Draw the horizontal and vertical lines according to the scale;
4. Plot the points and join them by straight line; and
5. Write the title and the scale.

Example. Average temperature for Chololo village, in Dodoma from 2010 to 2018

Year	2010	2011	2012	2013	2014	2015	2016	2017	2018
Temperature in °C	28.7	28.2	29	28.2	29.3	31.9	32.2	32.4	32.2

Solution Scale: V.S: 1 cm to 1°C and H.S: 1 cm to 1 year Simple line graph showing trend of annual mean temperature in Oc for Chololo village, in Dodoma (2010-2018)

Advantages of using simple line graphs

1. Easy to Understand: Line graphs are simple and show trends clearly over time, making them easy for students to follow.
2. Shows Trends: They are great for showing how things change, such as population growth or rainfall patterns.
3. Quick Comparisons: Multiple lines can be added to compare different datasets easily.
4. Visually Appealing: The graph format is neat and helps students grasp the relationship between variables quickly.
5. Good for Continuous Data: It works well with data like temperature, sales, or other data measured over time.

Disadvantages of using simple line graphs

1. Limited Detail: Line graphs don’t show detailed breakdowns of data, so small variations might be missed.
2. Confusing with Many Lines: If too many lines are added, the graph can become hard to read.
3. Not Ideal for Non-Continuous Data: It doesn’t work well with categories or data that aren’t measured over time.
4. Requires Accurate Plotting: Errors in plotting points or drawing lines can give the wrong impression of trends.
5. Misleading with Small Differences: If the scale isn’t chosen carefully, it can make small changes look bigger or smaller than they are.

Group line graphsGroup line graphs also known as comparative or multiple grouped line graphs are graphs which present more than one item or series of data. Group line graphs display the relationship between sets of similar statistics for two or more items. Note that the drawn line should not be uniform and on the other hand presentation of five lines per graph is recommended. ProceduresThe following are procedures for constructing multiple line graphs

1. Identify the variables from the given data;
2. Identify the item with highest value and use it to choose the scale;
3. Draw the horizontal and vertical lines;
4. Plot the points and join them with lines of different texture or colour; and
5. Write the title, scale and show the key.

**Example.**Annual mean temperatures from five stations in Tanzania from 2012 to 2016

Station	Years
	2012	2013	2014	2015	2016
Kilimanjaro (KIA)	30.8	30.3	29.7	30.4	30.1
Dar es Salaam (JNIA)	32.2	32.1	32.0	32.0	31.3
Mtwara	30.6	31.0	30.7	31.1	30.9
Songea	26.7	27.3	26.7	27.7	28.0
Mbeya	25.1	24.6	23.7	26.2	24.0

Solution Scale: V.S: 1 cm to 5°C and H.S: 2 cm to 1 year Multiple line graph for the trends of annual mean temperature in OC from five stations in Tanzania from 2012 to 2016

Advantages of using multiple/group/comparative line graphs

1. Good for Comparisons: Multiple line graphs help compare trends between two or more datasets, like comparing rainfall in different regions.
2. Shows Relationships: They allow students to see how different variables relate to each other over time.
3. Efficient Display of Data: Many sets of data can be shown on one graph, saving space and time.
4. Highlights Differences: Students can easily spot which dataset has higher or lower values over time.

Disadvantages of using multiple/group/comparative line graphs

1. Can Be Confusing: Too many lines on one graph can make it hard for students to follow, especially if the lines are close together.
2. Difficult to Interpret: If lines cross each other, it might be tricky for students to understand the changes clearly.
3. Requires Accurate Key/Legend: Without a clear key, students might mix up which line represents which dataset.
4. May Hide Small Changes: With multiple lines, small differences between datasets might not stand out.
5. Needs Careful Scaling: Poor choice of scale can make the data harder to read or mislead students.

Compound line graphsCompound line graphs also known as composite cumulative or divided line graphs are drawn with several different components. On a compound line graph, the differences between the points on adjacent lines give the actual values. It is a good alternative to grouped line graph because the procedures for constructing are the same. The only difference is that instead of drawing lines in different colour or shade, they are all shown in bold form but the space between one line and the other is shaded differently. It is commonly suggested that values should be arranged in a certain order, with the highest values at the top and lower value at the bottom. Lines should not cross each other and data should be arranged in a cumulative manner. ProceduresThe following are procedures for constructing compound line graph

1. Prepare a cumulative table by adding individual items to previous items;
2. Draw the x and y axes and choose a suitable horizontal and vertical scale;
3. Plot the dots for cumulative values of independent variables corresponding with the dependent variables from each item by rearranging from largest to smallest or vice versa. This rearrangement should be for the first year then in other years items should follow the order of the first year;
4. Join the dots with portions of straight lines;
5. The area occupied by each component presented on the graph, has to be coloured or shaded differently so as to give a clear distinction between the components;
6. Always start with the item with highest value and end with item with lowest value or vice versa;
7. Lines should not cross each other and data should be arranged in a cumulative manner; and
8. Write the title, scale and key.

**Example.**Electricity generation in Giga Watt per hour in Tanzania from 2011 to 2017

Year Fuel source	2011	2012	2013	2014	2015	2016	2017
Hydro	1992.6	1769.9	1721.3	2613.5	2124.4	2382.1	2369.1
Gas	2265	2664	2872.2	2624	2873.8	4196.4	4322
Diesel	781.1	1083.5	1133.2	784.9	1188.2	389.1	294.4

SolutionCumulative table for EGW per hour in Tanzania 2011 – 2017

Year	2011	2012	2013	2014	2015	2016	2017
Fuel source
Gas	2 265	2 664	2 872.2	2 624	2 873.8	4 196.4	4 322
Hydro	4 257.6	4 433.9	4 593.5	5 237.5	4 998.2	6 578.5	6 691.1
Diesel	5 038.7	5 517.4	5 726.7	6 022.4	6 186.4	6 967.6	6 985.5

  **Scale :**V.S : 1cm to 1000 GWh and H.S: 2cm to 1 year Compound line graph for electricity generation in giga watt per hour in Tanzania from 2011 to 2017

Advantages of using compound/ composite cumulative / divided line graphs

1. Shows Total and Parts: A compound line graph shows the total value as well as how different parts (categories) contribute to it. For example, it can show the total population and how different age groups make up that population.
2. Good for Trends: It helps students see how the total and its parts change over time.
3. Visually Clear: By stacking the lines, it is easier to compare the size of each part within the total.
4. Useful for Categories: It works well when data is divided into groups, like income from different sectors over time.

Disadvantages of using compound/ composite cumulative / divided line graphs

1. Hard to Interpret: Students might find it challenging to understand how the parts contribute to the total if the graph is not explained well.
2. Confusing with Many Categories: If there are too many categories, the graph can become cluttered and hard to read.
3. Requires Accurate Plotting: Errors in stacking the lines can lead to incorrect interpretation of the data.
4. Difficult to Compare Parts Directly: Unlike other graphs, comparing individual categories across years might not be very straightforward.
5. Scaling Issues: Choosing an inappropriate scale can make small contributions look insignificant or exaggerate them.

Divergent line graphIt is used to show fluctuations in value in terms of “positives” or “negatives” also known as ‘profits or losses’, ‘gains or losses’ and ‘increases or decreases’. Such fluctuations are common in imports and exports, population trends, production of goods and commodities. The graph, can also address the increase and decrease pattern of temperature and rainfall trends. As such it can be used by climatologists, meteorologists and geographers in drawing insights on the extent of extreme weather events, climate change and variability as well as their effects to environment and welfare. ProceduresThe following are the procedures for construction of divergent line graph

1. Find the sum of the number of observations in the set of data;
2. Calculate the mean;
3. Subtract the mean from each data/value given;
4. Plot the divergences (positive and negatives) on a graph with positive on the upper part of mean (zero) line and negatives below it by putting dots; (zero) line must be bolded; and
5. Finally join the dots sequentially. The zero line represent the mean on one side of (zero) line should indicate the mean.

**Example.**Average temperature for Chololo village, in Dodoma from 2010 to 2018

Year	2010	2011	2012	2013	2014	2015	2016	2017	2018
Temp. in °C	28.7	28.2	29	28.2	29.3	31.9	32.2	32.4	32.2

SolutionAverage temperature for Chololo village, in Dodoma from 2010 to 2018

Year	Temperature (xi)	$\overline{x}$	$x_i - \overline{x}$
2010	28.7	30.2	−1.5
2011	28.2	30.2	−2
2012	29	30.2	−1.2
2013	28.2	30.2	−2
2014	29.3	30.2	−0.9
2015	31.9	30.2	1.7
2016	32.2	30.2	2
2017	32.4	30.2	2.2
2018	32.2	30.2	2

$\sum_{i=1}^{n} x_i = 272.1$

  Recall mean is given by

The image shows the calculation of the mean ($\bar{x}$) of a dataset. The formula for the mean is given by:

$$\bar{x} = \frac{\sum_{i=1}^{N} x_i}{N}$$

From the image, we can see the following:

• The sum of the data points ($\sum_{i=1}^{N} x_i$) is equal to $272.1$.
• The number of data points ($N$) is equal to $9$.

Substituting these values into the formula, we get:

$$\bar{x} = \frac{272.1}{9} = 30.2$$

Therefore, the mean of the dataset is $30.2$.

The calculated mean is used in computing the deviation as shown in Table above Scale: V.S 1 cm to 0.5 Temperature °C and H. S 1 cm to 1 year The divergent line graph for the average temperature for Chololo village, in Dodoma from 2010 to 2018

Advantages of using  divergent line graphs

1. Shows Positive and Negative Trends: Divergent line graphs are great for showing changes above and below a central point (e.g., profits and losses or temperature changes from a baseline).
2. Easy to Compare Opposites: They make it easy to compare opposing values, like growth versus decline.
3. Highlights Extremes: Students can quickly see the highest and lowest points on either side of the central axis.
4. Good for Balance Analysis: They help students analyze situations where balance or imbalance is important, like exports versus imports.

Disadvantages of using  divergent line graphs

1. Can Be Confusing for Beginners: Students might struggle to interpret the graph if they are not familiar with the concept of a central axis or negative values.
2. Requires Careful Labeling: Without clear labels and explanations, it can be hard to tell which side of the graph represents positive or negative values.
3. Not Suitable for All Data: Divergent line graphs are only useful when there is a meaningful central point (e.g., zero or an average baseline). They don’t work well for general trends.
4. Cluttered with Multiple Lines: Adding too many datasets can make the graph messy and hard to follow.
5. Needs Accurate Scaling: Poor scaling can exaggerate small differences or make important details hard to see.

Bar graphsBar graph also known as a column graph refers to an x-y graph showing the tendencies of rainfall, population and other quantities like goods. Each tendency is shown by a column or bar whose length or height represents its value along y-axis. The purpose of the graph is to show numerical facts in visual form so that they can be understood quickly, easily and clearly. Bar graphs are appropriate when there is a need to present trends or comparison. In showing comparison it may consist of two or more parallel verticals (or horizontal) bars or rectangles.

1. Simple bar graph
2. group bar graph
3. compound bar graph
4. divergence bar graph.

Simple bar graphsSimple bar graphs consist of parallel, usually vertical bars or rectangles with length proportional to the frequency with which specified quantities occur in a set of data. It can be defined as quantitative comparison by rectangles with lengths proportional to the measure of the data or things being compared. It can be drawn to show rainfall and total exports or imports. ProceduresThe following are procedures for constructing simple bar graph

1. From the given data, identify the types of variables;
2. Select the suitable scale;
3. Draw horizontal and vertical line and construct bars vertically above the horizontal lines;
4. Shade the bars equally;
5. Write the title and the key;
6. On a graph, draw two lines perpendicular to each other, intersecting at zero;
7. The horizontal line is x-axis and vertical line is y-axis;
8. Along the horizontal axis, choose the uniform width of bars and uniform gap between the bars and write the names of the data items whose values are to be marked;
9. Along the vertical axis, choose a suitable scale in order to determine the heights of the bars for the given values. (Frequency is taken along y-axis); and
10. Calculate the heights of each bar according to the scale chosen and draw the bars.

**Example.**Hydroelectric power generation Giga Watt per hour (GWh) in Tanzania from 2011 to 2017

Year	2011	2012	2013	2014	2015	2016	2017
GWh	1992.6	1769.9	1721.3	2613.5	2124.4	2382.1	2369.1

solution Scale: V. S 1cm to 500 GWh and H.S: 1cm to 1 year Simple bar graph for hydroelectric power generation in GWh in Tanzania from 2011 to 2017

Advantages of using simple bar graphs

1. Easy to Understand: Bar graphs are straightforward and visually clear, making them ideal for beginners.
2. Good for Comparisons: They make it easy to compare different categories, such as the number of students in different classes.
3. Can Show Exact Values: By reading the height or length of a bar, students can see the exact value being represented.
4. Flexible Use: Simple bar graphs work well for both small and large datasets.
5. Visually Appealing: They are neat and easy to draw, especially when students use graph paper.

Disadvantages of using simple bar graphs

1. Not Suitable for Trends: Bar graphs cannot show changes over time effectively; a line graph is better for that.
2. Cluttered with Many Categories: If there are too many bars, the graph becomes crowded and harder to read.
3. Limited for Large Data Ranges: When values vary widely, it may be difficult to choose a scale that represents the data clearly.
4. Cannot Show Relationships: Bar graphs are not good at showing connections between different variables.
5. Requires Accurate Scaling: Errors in scaling or drawing bars can lead to misinterpretation of the data.

Grouped bar graphGrouped bar graph also known as comparative or multiple bar graph is where two or more simple bars are grouped side by side on the same vertical scale for the sake of comparison. It is a graph that uses rectangular bars to represent different values for showing comparisons among categories such as the amount of rainfall in different months of a year, or the average salary in different states. Grouped bar graphs are commonly drawn vertically, though they can also be depicted horizontally. ProceduresThe following are procedures for construction of group bar graph

1. Draw and label the vertical and horizontal sides (axes);
2. Choose a scale that suits the data;
3. Place dots on the graph to represent the data;
4. Connect the dots in order;
5. Write a title above the graph;
6. To give an impression of totality, bars are usually drawn touching each other that is without a gap between them, but attention may be drawn to individual components by leaving a small space between the bars. Also, groups of bars must be separated from each other with similar space or gap;
7. It is a custom to draw the bars of each group in ascending or descending order for comparison purposes;
8. All bars must be of the same width and drawn at right angles to the axis; and
9. Write the title, scale and show the key

**Example.**Electricity generation in Giga Watt per hour in Tanzania from 2011 to 2017

2011	2012	2013	2014	2015	2016	2017
1992.6	1769.9	1721.3	2613.5	2124.4	2382.1	2369.1
2265	2664	2872.2	2624	2873.8	4196.4	4322
781.1	1083.5	1133.2	784.9	1188.2	389.1	294.4

solution Scale: V. S: 1 cm to 500 GWh and H.S: 1.5 cm to 1 year Grouped bar graph for electricity generation in Giga Watt per hour in Tanzania from 2011 to 2017

Advantages of using grouped bar graph

1. Good for Comparisons: Grouped bar graphs allow students to compare data within and between groups, like comparing boys' and girls' performance in different subjects.
2. Visually Clear: Bars are grouped side by side, making it easy to see differences between categories.
3. Shows Relationships Between Groups: Students can observe patterns, such as how one group performs compared to another.
4. Useful for Multiple Variables: It works well when comparing two or more datasets, like rainfall in several regions over different months.
5. Easy to Interpret: With proper labeling, grouped bar graphs are simple to read and understand.

Disadvantages of using grouped bar graph

1. Can Be Crowded: Too many groups or bars can make the graph cluttered and hard to read.
2. Requires a Clear Key/Legend: Without a clear legend, students might confuse which bar represents which group.
3. Not Suitable for Large Data: With many datasets, the graph may become overly complex and lose clarity.
4. Difficult to Compare Across Groups: It can be hard to compare specific values when bars are close in height or length.
5. Requires Accurate Plotting: Mistakes in spacing or scaling can make the graph misleading or hard to interpret.

Compound bar graphCompound bar graph refers to a graph which combines two or more types of information in one graph. It can also compare different quantities. A compound bar graph is a type of bar chart where columns can be split into sections to show breakdown of data. It is drawn by subdividing one bar into component parts. The total length of the bar represents the total value of the entire component in which parts are shown in such division. ProceduresThe following are procedures for constructing compound (divide) bar graph.

1. Identify the types of variables;
2. Find the item with the highest total;
3. Prepare the cumulative table and enter the values cumulatively starting with the highest or the smallest to largest item. This rearrangement should be for the first year and the following years should follow the established order;
4. Use the highest total among the total in the table to select a suitable vertical scale. For the case of horizontal scale, the number of items of independent variable should be considered;
5. Draw the vertical and horizontal lines;
6. Draw bars vertically above the horizontal line,the height of each depends on its total in the cumulative table;
7. Divide and shade bars, accordingly; and
8. Write the title, scale and the key.

**Example.**Electricity generation in Giga Watt per hour in Tanzania from 2011 to 2017

	2011	2012	2013	2014	2015	2016	2017
Hydro-electric power	1992.6	1769.9	1721.3	2613.5	2124.4	2382.1	2369.1
Gas	2265	2664	2872.2	2624	2873.8	4196.4	4322
Diesel/heavy Fuel Oil/Gas oil	781.1	1083.5	1133.2	784.9	1188.2	389.1	294.4

solution Scale: V.S: 1cm to 1000 GWh and H.S: 1cm to 1 Year Compound bar graph for an electricity generation in Giga watt per hour in Tanzania from 2011 to 2017

Advantages of using compound bar graph

1. Shows Total and Parts: Compound bar graphs display the total value and how different parts (categories) contribute to it. For example, it can show total school enrollment and the contribution of boys and girls.
2. Good for Comparing Categories: Students can easily compare different groups, like the contribution of various crops to total agricultural output.
3. Visually Clear for Stacked Data: By stacking bars, it’s easy to see how the parts add up to form the total.
4. Efficient Representation: It saves space by showing all data in one bar per group, instead of multiple bars.
5. Highlights Proportions: It helps students analyze the proportions of parts within a total.

Disadvantages of using compound bar graph

1. Difficult to Interpret: It can be hard for students to understand individual parts if they are not well-labeled or if the bars are too small.
2. Cluttered with Many Categories: When there are too many parts, the graph can become crowded and confusing.
3. Not Ideal for Detailed Comparisons: Comparing specific parts across groups is harder than with grouped bar graphs.
4. Scaling Issues: Poor scaling can make smaller parts look insignificant or exaggerate their size.
5. Requires Careful Labeling: Without a clear legend or key, students may misinterpret the parts of the graph.

Divergent bar graphsIn this type of graphs, data spread is both positive and negative and it is displayed divergently. These could be constructed on either the x or y axis. Divergent bar graphs are used when one set of data is provided for part of the period under consideration and then this dataset is split into separate components for another part of the period ProceduresThe following are procedures for constructing divergent bar graph.

1. Find the sum of the number of observations in the set of data;
2. Calculate the mean;
3. Subtract the mean from each data or value given to get deviation;
4. Select a suitable vertical and horizontal scales;
5. Plot the divergences (positive and negatives) on a graph with positive on the upper part of mean (zero) line and negatives below it by putting dots; zero line must be bold;
6. Draw bars up and down the line of average and shade them equally; and
7. Write the title, and scale.

Note: The zero line must be clearly indicated usually by thickening. As the bar, the horizontal scale is in fact best written at the bottom and top of the graph. The vertical axis must be scaled both above and below the zero line, the upper part for positive and the lower for negative values. **Example.**Passengers transport in thousand (‘000) by the Tanzania Railways from 2010 to 2015

Year	2010	2011	2012	2013	2014	2015
Passengers in thousand	284	227	339	373	170	196.4

solutionPassengers transport in thousand (‘000) by the Tanzania Railways from 2010 to 2015

Year	Total number of passengers in '000 thousand (xi)	$\bar{x}$	xi - $\bar{x}$
2010	284	264.9	19.1
2011	227	264.9	-37.9
2012	339	264.9	74.1
2013	373	264.9	108.1
2014	170	264.9	-94.9
2015	196.4	264.9	-68.5

$$\sum_{i=1}^{n} x_i = 1589.4$$

The mean is obtained by:

Based on the image, the calculation of the mean ($\bar{x}$) is: The formula is:

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

From the first image, the values are:

• $\sum_{i=1}^{n} x_i = 1589.4$
• $n = 6$

So, the mean is:

$$\bar{x} = \frac{1589.4}{6} = 264.9$$

From the second image, the values are:

• $\sum_{i=1}^{N} x_i = 272.1$
• $N = 9$

So, the mean is:

$$\bar{x} = \frac{272.1}{9} = 30.2$$ **Scale:** V.S: 1 cm to 20 passengers H.S: 1 cm to 1 year The divergent bar graph for passengers transport in thousand (‘000) by the Tanzania Railways from 2010 to 2015

Advantages of using divergent bar graphs

1. Shows Positive and Negative Values: Divergent bar graphs are great for showing data that has both positive and negative values, like profit and loss or temperature above and below zero.
2. Highlights Differences Clearly: Students can easily see how much one side (e.g., positives) differs from the other (e.g., negatives).
3. Good for Balance Analysis: It helps students analyze situations where a balance or comparison is important, like imports versus exports.
4. Visually Appealing: The bars extending in opposite directions make it easy to understand the contrasts.
5. Useful for Comparisons: It allows comparison of two opposing categories side by side, such as male and female population growth.

Disadvantages of using divergent bar graphs

1. Can Be Confusing for Beginners: Students may struggle to interpret data if they are not familiar with the concept of divergence or central axes.
2. Requires Accurate Scaling: Errors in scaling can exaggerate or hide differences between values.
3. Limited to Specific Data: It is only suitable for data that naturally has opposing categories, like gains versus losses, and cannot be used for general comparisons.
4. Hard to Read with Many Categories: Too many bars can make the graph cluttered and difficult to interpret.
5. Needs Clear Labeling: Without proper labels and a key, it can be hard for students to understand what each side of the graph represents.

A combined line and bar graphSometimes a simple line and a bar graph may be combined in the same graph to show more often climate data such as temperature and rainfall. This type of graph is termed as a climograph. Procedure: The following are procedures for constructing a combined line and bar graph. Similar procedure for the construction of simple line and bar graphs need to be used to construct a combined line and bar graph. Note: You may choose a different scale for rainfall and temperature. In this case as well, rainfall will be in bars as shown but temperature is plotted in line which is above the bars. **Example.**Data for temperature and rain fall recorded at station X in Ikombe Village.

Months	J	F	M	A	M	J	J	A	S	O	N	D
Temp. °C	26	27	29	28	28	27	25	25	28	27	28	26
Rainfall	240	230	220	190	175	180	215	210	195	180	200	210

solution Scale: HS: 1 cm to 1 month, VS for Temp: 1 cm to 2 °C, V.S for Rainfall: 1 cm to 20 mm A combined line and bar graph (Climograph) for station X

Advantages of using combined line and bar graphs

1. Shows Two Types of Data Together: A combined line and bar graph can show trends (line) and quantities (bars) in one graph, making it easier to understand relationships.
2. Good for Comparisons: Students can compare how one variable (e.g., rainfall) affects another (e.g., crop yield).
3. Saves Space: Instead of using two separate graphs, both datasets are displayed in one, making it efficient.
4. Visually Clear: With proper labeling, it is easy to differentiate between the line and bar data.
5. Flexible: It works for a variety of data types, such as showing population growth (line) and annual income (bars).

Disadvantages of using combined line and bar graphs

1. Can Be Confusing for Beginners: Students may struggle to interpret the graph if they don’t understand the difference between the line and bar data.
2. Requires Clear Key and Labels: Without proper labeling, it can be hard to tell which dataset is represented by the line and which by the bars.
3. Not Ideal for Complex Data: If there are too many lines or bars, the graph can become cluttered and hard to read.
4. Scaling Issues: If the line and bar data have different units or ranges, choosing an appropriate scale can be challenging.
5. Needs Accurate Plotting: Mistakes in plotting either the bars or the line can lead to incorrect conclusions.

Age - sex graphA population pyramid also known as age and sex pyramid, population structure or age and sex structure refers to the geographical representation of age structure or distributions of population according to age groups.The graph is commonly used by demographers. Demographers identify three types of pyramids namely: expansive or rapid growth, stationary or slow growth and constrictive or contractive or negative growth pyramids. The structure of the pyramids is dynamic depending on the changes of population structure. The demographics are changing from pyramid and finally to barrel which end the point of population pyramids. Types of population pyramids The graphical representation of the population pyramids ultimately relies on age and sex structure of a given population. Such shapes may take the form of a triangular pyramid, have a columnar or rectangular (with vertical sides rather than sloped sides), or have an irregular profile. Below are the major categories of population pyramids:

1. expansive pyramid
2. stationary pyramid
3. constrictive pyramid
4. compounded population pyramid

Expansive pyramid This is also known as rapid growth pyramid. It has a broad base with successive decline in the share of population of higher age groups. The pyramid represents a relatively high fertility and mortality rates; low life expectancy; higher population growth rates; and low share of old age persons. The pyramids portray the expansion of population as the size of each cohort gets larger than the size of the same in previous time. Expansive age pyramids are common for developing countries mainly in Africa and Asia. In drawing population pyramids, you should consider the following.

1. The age groups, are usually based on quinquennial (5years) periods (0 - 4, 5 - 9, 10 - 14) while the youngest age group forming the base of the graph;
2. In calculating percentage, two methods are possible either the individual male or female population or each group may be calculated as percentages of the total population; and
3. It should be noted that the procedures for constructing the population pyramids are common across all types of pyramids. The shapes of resultant pyramids are also the result of a population composition at a particular time and space.

Procedures The following are the procedures for constructing age and sex pyramids graph

1. Identify types of variables and suggest suitable scales. For vertical scale, consider the number of age groups, and for the horizontal scale, consider the highest value or percent;
2. Draw two vertically standing lines of not more than 2cm apart however, 2 cm wide is suitable; at the centre of the graph paper;
3. From the bottom of the lines, are two horizontal lines away from each other to represent the sex. Male is predominately on the left while female on the right side;
4. The bars are drawn horizontally and their length correspond to the size of the age groups. It is in fact a comparative bar graph drawn horizontally; and
5. Shade the bars, write the title and indicate the scale.

Example Study the data provided in Table  below which show the distribution of population by age and sex then construct age and sex graph by using absolute value. Population distribution by age and sex based on 2012 census survey

Age group	Male	Female
0 - 4	3 535 673	3 534 222
5 - 9	3 242 111	3 233 253
10 - 14	2 809 113	2 816 735
15 - 19	2 171 355	2 295 319
20 - 24	1 737 849	2 093 249
25 - 29	1 503 841	1 789 025
30 - 34	1 342 110	1 485 372
35 - 39	1 149 418	1 219 682
40 - 44	916 020	924 316
45 - 49	694 318	759 147
50 - 54	587 555	585 004
55 - 59	39 627	371 783
60 - 64	368 814	380 318
65 - 69	232 811	248 460
70 - 74	220 651	245 426
75 - 79	149 974	145 122
80+	2 060 73	259 608

solution

1. **By the use of absolute value **Scale: H.S: 1 cm to 100 000 and V.S: 0.5 cm to 1 barPopulation pyramid of Tanzania mainland in 2012 census survey

2. By the use of percentage value

   Age group	Male	Female	Total	%Male	%Female
   0 - 4	3 535 673	3 534 222	7 069 895	8.103	8.100
   5 - 9	3 242 111	3 233 253	6 475 364	7.430	7.410
   10 - 14	2 809 113	2 816 735	5 625 848	6.438	6.455
   80+	2060 73	259 608	465 681	0.472	0.595
   Total	21 247 313	22 386 041	43 633 354	50	50

   solution Scale: H.S: 1 cm to 1% and V.S: 0.5 cm to 1 barAge and sex pyramid of Tanzania mainland in 2012 census Survey

Stationary pyramidThis is also, known as slow growth curve. Stationary pyramids are the pyramids describing a constant share of population in different age groups over the period of time. They displays a situation with low fertility and mortality rates and high life expectancy. They depict a slow population growth or stable population. The stationary or near stationary population pyramid displays some what equal share of juvenile and adult age groups. Stationary pyramid Constrictive pyramidThis is also known contractive or negative growth pyramid. It is a pyramid with a narrow base. It displays a low fertility and mortality rate, life expectancy and ageing of population are high. The pyramids are typically common in developed countries where they have a high level of literacy, access to birth control measures and quality health care associated with improved medical facilities. Constrictive pyramid

Advantages of age sex /population pyramid graphs

1. Shows Population Structure: A population pyramid clearly shows the distribution of a population by age and sex, making it easy to understand the age groups and gender proportions.
2. Easy to Compare Different Populations: It allows students to compare the population structures of different regions or countries, such as comparing the population of Tanzania to that of another country.
3. Highlights Growth Patterns: Students can quickly see if a population is growing, stable, or shrinking by looking at the shape of the pyramid (e.g., wide base means high birth rate).
4. Shows Dependency Ratios: It helps students understand the number of people who depend on others, like children and the elderly, by showing the age distribution.
5. Visually Clear: The graph is easy to interpret with labeled age groups on the y-axis and population size on the x-axis.

Disadvantages of age sex /population pyramid graphs

1. Limited to Specific Data: Population pyramids only work with demographic data, and cannot be used for other types of data analysis.
2. Can Be Misleading: If the population data is not accurate, the pyramid can give a false impression of the population structure.
3. Hard to Compare Complex Data: It may be difficult to compare complex data or multiple factors (e.g., employment rates, education) in a population pyramid.
4. Not Detailed: A population pyramid does not show detailed information about individuals or small subgroups within the population.
5. Requires Proper Labeling and Interpretation: Without clear labeling, students may confuse different age groups or misinterpret the data, especially if there are many categories.

A compounded population pyramid This is also referred to as superimposed population pyramid. It is a population pyramid which comprises different population categories superimposed in one bar. Procedures The following are procedures for constructing a compounded pyramids graph

1. Identify the types of variables for this case age,sex and employment variable and suggest suitable scales;
2. Draw two vertically standing lines of not more than two (2cm) apart;
3. The bars of sex and employment are drawn horizontally and their lengths correspond the size of the age groups; and
4. Other procedures are as in constructing the normal population pyramids

**Example:**Study the data provided in Table below then draw a comparative population structure to represent the following data for country x. Data for population structure and employment for country x

Age group	Total population		Population in employment
	Male	Female	Male	Female
20 - 24	85 000	100 000	60 000	50 000
25 - 29	70 000	80 000	50 000	30 000
30 - 34	60 000	74 000	52 000	52 000
35 - 39	52 000	62 000	48 000	30 000
40 - 44	44 000	48 000	30 000	20 000
45 - 49	30 000	32 000	25 000	25 000
50 - 54	23 000	28 000	15 000	16 000
55 - 59	15 000	16 000	8 000	5 000
60 - 64	10 000	12 000	5 000	8 000
65 - 69	5 000	8 000	2 000	2 000

solution Compounded population structure of country x

Advantages of using compound population pyramid

1. Shows More Detailed Data: A compound population pyramid combines two populations (e.g., male and female) or shows multiple age groups, making it easy to compare them at the same time.
2. Helps Analyze Gender Differences: It clearly shows the difference between male and female populations across age groups, helping students understand gender distribution.
3. Shows Age Distribution in Depth: It provides a more detailed view of age groups and their proportions in the total population, which can show trends like youth bulges or aging populations.
4. Useful for Comparing Multiple Groups: Students can use it to compare more than one population or area, like comparing urban and rural populations within the same country.
5. Clear Visual Representation: The structure of the pyramid helps students quickly identify patterns, like a growing or shrinking population, or the balance between different age groups.

Disadvantages of using compound population pyramid

1. Can Be Complex to Interpret: Students may find it difficult to understand if there are many age groups or if the pyramid is overcrowded with data.
2. Needs Clear Labeling: Without proper labeling and a key, students might confuse the different populations or age groups represented in the pyramid.
3. Not Suitable for Other Types of Data: Compound population pyramids are limited to demographic data and cannot be used for other types of analysis, like economic or educational data.
4. Can Be Misleading with Poor Data: If the data is inaccurate or outdated, it can give an incorrect view of the population structure.
5. Requires Proper Scaling: Choosing the right scale for both populations (e.g., male and female) is essential. If the scale is incorrect, the pyramid may not accurately represent the data.

Circular graphA circular graph is also known as dispersion, clock or polar graph due to its resemblance to the face of a clock or lines of longitude radiating from the pole. The analogy between the twelve months of the year and the twelve hours of the clock face adds attraction to the use of this type of graph. It is mostly used to show farmers the seasonal calendar in a year for farmers. Procedures The following are procedures for constructing a circular graph

1. Identify the types of variables and select a suitable scale;
2. Draw seven concentric circles, the smallest at the center should be not more than 2 cm in diameter; However, it depends on the size of the paper. Distance from one circle to another should be 1cm;
3. Draw 12 radii of 30° apart, starting from 12 o’clock radius clockwise. The 12 radii stand for months of the year, named clockwise from the 12 o’clock radius;
4. Along the radii, draw bar for rainfall;
5. For temperature, plot the points and join them with a curved line;
6. Write the title, key and scale. Remember vertical scale represents rainfall and temperature, while horizontal scale represents months;
7. As clock graph is frequently used to represent climatic statistics, radii are scaled in °c .The scale is indicated on either the 12 o’clock or 6 o’clock radius. Points plotted are then joined as a continuous circle;
8. Bar can also be drawn along the radii to indicate monthly mean rainfall. In order to avoid congestion at the centre of the circle, zero is normally represented as a circle; and
9. Write the title, scale and key.

ExampleStudy the data provided in Table below  and draw a polar chart. Monthly mean rainfall (mm) and temperature (°C) in Tanzania in 2016

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Temp ºC	28.4	28.9	29.8	27.9	27.9	27.3	26.8	28.1	28.5	29.9	29.6	28.5
Rainfall (mm)	191.8	131.2	140	213.6	41.1	9.2	2.2	8.3	14.1	27.8	64.6	66.6

solution Polar chart for monthly mean rainfall and temperature in Tanzania in 2016

Advantages of using polar charts

1. Shows Data in a Circular Way: Polar charts are useful for displaying data that has a direction or angle, such as wind direction or the hours of sunlight throughout the day.
2. Easy to Compare Categories: It allows students to compare data points at different angles or directions. For example, comparing the temperature across different months.
3. Visually Interesting: The circular format is visually appealing and can make the data more engaging for students.
4. Good for Showing Cyclical Data: Polar charts are excellent for displaying patterns that repeat, such as seasons, daily routines, or sales trends over a week.
5. Clear Representation of Proportions: The size of each section or “slice” clearly shows the proportion of each category relative to the whole dataset.

Disadvantages of using polar charts

1. Can Be Hard to Read: For beginners, polar charts can be difficult to interpret, especially if there are many categories or data points.
2. Requires Accurate Labeling: Without clear labeling and a legend, students might struggle to understand what each section represents.
3. Not Suitable for Complex Data: Polar charts are not ideal for datasets with a lot of categories or detailed numerical values, as they can become cluttered.
4. Difficult to Compare Precise Values: It can be harder to compare specific values across different categories, especially if the angles are close together.
5. Limited Use for Non-Cyclical Data: Polar charts are mainly useful for showing data that has a repeating cycle or pattern. They are not well-suited for general data comparisons.

Statistical charts and diagramsStatistical charts and diagrams methods differ from statistical graphs as they do not depend on squared paper or a map in data presentation. Rather they display data in circular graphs, rectangles, repeated symbols, proportional diagrams, graduated symbols and wind roses.They may be used in conjunction with a map for the purpose of defining or describing a location but they can also be drawn independently. They are not necessarily drawn on a graph paper but even plain or ruled papers. There are six (6) major statistical charts and diagrams, which include:

1. divided circles(pie charts)
2. divided rectangles,
3. repeated symbols,
4. proportional diagrams
5. graduated range of symbols
6. windroses.

Divided circleDivided circle also known as pie chart refers to a diagram consisting of a circle divided into the slices which are proportional in size to the value represented. The slice of the circle may be shaded or coloured and labeled. The largest slice is plotted first clockwise from 12 o’clock in ascending order for easy comparison. The divided circle can be sub-divided into three parts namely simple divided circle (pie chart), proportional divided circles and proportional divided semi-circles. Simple divided circleIt is a simple pie chart which is used to represent simple data such as exports, imports or production. Simple divided circle is also known as simple pie chart. ProceduresThe following are procedures for constructing simple divided circle

1. Find the total amount of all values;
2. Change each of the values into percentage, and then into degrees;
3. Draw the circle of suitable radius;
4. Divide the circle into parts corresponding to the value of each radius of respective components. Drawing should be done clockwise from the 12`starting with the highest degree value;
5. Shade each portion differently; and
6. Write the title and the key.

Note: The circle may be of any convenient size, too small circle must be avoided. ExampleData in Table below which show mineral imports in (‘000) metric tonnes in Tanzania in 2015 have been used to draw . Mineral imports (‘000) metric tonnes in Tanzania in 2015

Mineral type	Weight in '000 tonnes
Coal	269
Gypsum	38
Petroleum	52
Clinker	50

SolutionPercentage of mineral importation in (‘000) metric tonnes in Tanzania in 2015

Mineral type	Weight in '000 (Xi)	$\frac{X_i}{\sum_{i=1}^{n}X_i} \times 100\%$	$\frac{\%}{100\%} \times 360^\circ$
Coal	269	66%	237.6^o^
Gypsum	38	9%	32.4^o^
Petroleum	52	13%	46.8^o^
Clinker	50	12%	43.2^o^
Total	409	100%	360^o^

  Mineral imports in (‘000) metric tonnes in Tanzania in 2015

Advantages of using pie chart

1. Easy to Understand: Pie charts are simple to read and understand, making them ideal for beginners. They show parts of a whole in a clear, visual way.
2. Good for Showing Proportions: They help students quickly see how different parts contribute to the total, such as the percentage of votes for different political parties.
3. Visually Appealing: The circular shape of a pie chart is visually engaging and helps in making comparisons between categories more intuitive.
4. Useful for Small Data Sets: Pie charts work best with a small number of categories (less than 6 or 7), making them perfect for showing simple data distributions, like the market share of companies.
5. Clear Representation of Percentages: The size of each slice of the pie directly corresponds to the percentage or proportion it represents, which is easy for students to understand.

Disadvantages  of using pie chart

1. Limited to Few Categories: Pie charts become hard to read when there are too many categories. More than 6 or 7 slices can make the chart look cluttered.
2. Hard to Compare Similar Sizes: It can be difficult to compare slices that are close in size, especially if the chart has many small slices.
3. Not Suitable for Showing Trends: Pie charts are not effective for showing changes over time. For trends, line or bar graphs are better.
4. Can Be Misleading: If the data is not accurately represented or if the chart does not have clear labels, pie charts can give a misleading impression of the data.
5. Requires Accurate Labeling: Without clear labels or a key, it can be confusing for students to understand what each slice represents.

Proportional divided circleIt is a graph drawn in a circle whose radius is proportional to the total figures represented by all sectors of circle. They are used for showing a quantity (for example, population of a country) that can be divided into parts such as different ethnic groups. A circle is drawn to represent the total quantity. Two or more circles are drawn in such a way that each one is proportional to the value it represents. It is then divided into segments which are proportional in size to the components. The actual size of the circle can also be used to represent data. ProceduresThe following are procedures for constructing proportional divided circle

1. Find the total of each item under observation;
2. Compute the radius for each by applying the square roots on each of the total items under observation;
3. Determine the scale to be used;
4. Divide the calculated radii to the scale determined;
5. Draw the circle based on the calculated radii; and
6. Write the title and key

ExampleTrend of some of the wild animals hunted from 2009 to 2012

Year	Species
	Elephant	Lion	Leopard	Hippopotamus	Buffalo
2012	41	37	40	40	53
2011	45	27	44	38	47
2010	96	98	205	158	1108
2009	98	120	249	153	1061

SolutionTrend and total of some of the wild animals hunted from 2009 to 2012

Year	Elephant	Lion	Leopard	Hippopotamus	Buffalo	Total
2012	41	37	40	40	53	211
2011	45	27	44	38	47	201
2010	96	98	205	158	1108	1665
2009	98	120	249	153	1061	1681

The radii of two circles are determined by:

$\text{Radius}(R) = \sqrt{T}$

Where

$$\begin{aligned} &\text{T} = \text{the total value of the given item} \\ &R_1 = \sqrt{211} = 14.52 \\ &R_2 = \sqrt{201} = 14.17 \\ &R_3 = \sqrt{1665} = 40.80 \\ &R_4 = \sqrt{1681} = 41 \end{aligned}$$

Scale: Let 1cm represent 10 units (cm)

$$\begin{aligned} &14.52 \div 10 = 1.4 \text{ cm} \\ &14.17 \div 10 = 1.4 \text{ cm} \\ &40.80 \div 10 = 4 \text{ cm} \\ &41 \div 10 = 4.1 \text{ cm} \end{aligned}$$

To calculate the degrees

  Trend of some of the wild animals hunted From 2009 to 2012 in degrees

Year	Elephant	Lion	Leopard	Hippopotamus	Buffalo
2012	$\frac{41}{211} \times 360^\circ = 70^\circ$	$\frac{37}{211} \times 360^\circ = 63^\circ$	$\frac{40}{211} \times 360^\circ = 68^\circ$	$\frac{40}{211} \times 360^\circ = 68^\circ$	$\frac{53}{211} \times 360^\circ = 90^\circ$
2011	$\frac{45}{201} \times 360^\circ = 81^\circ$	$\frac{27}{201} \times 360^\circ = 48^\circ$	$\frac{44}{201} \times 360^\circ = 79^\circ$	$\frac{38}{201} \times 360^\circ = 68^\circ$	$\frac{47}{201} \times 360^\circ = 84^\circ$

2010	$\frac{96}{1665} \times 360^\circ = 21^\circ$	$\frac{98}{1665} \times 360^\circ = 21^\circ$	$\frac{205}{1665} \times 360^\circ = 44^\circ$	$\frac{158}{1665} \times 360^\circ = 34^\circ$	$\frac{1108}{1665} \times 360^\circ = 24^\circ$
2009	$\frac{98}{1681} \times 360^\circ = 21^\circ$	$\frac{120}{1681} \times 360^\circ = 26^\circ$	$\frac{249}{1681} \times 360^\circ = 53^\circ$	$\frac{153}{1681} \times 360^\circ = 33^\circ$	$\frac{1061}{1681} \times 360^\circ = 227^\circ$

Proportional divided circle showing trend of some of the wild animals hunted from 2009 to 2012 in degrees.

Advantages of using proportional divided circles

1. Shows Proportions Clearly: A proportional divided circle visually shows how a whole is divided into different parts, making it easy for students to understand how much each category contributes to the total.
2. Good for Comparing Sizes: It is easy to compare the relative sizes of different parts of the whole, such as comparing the percentage of the population in different age groups.
3. Visually Appealing: The circular shape can be more engaging than other types of charts, and students find it visually attractive.
4. Easy to Understand: Just like pie charts, proportional divided circles are simple and intuitive, making them suitable for beginners.
5. Useful for Showing Part-to-Whole Relationships: They work well when the data shows how individual parts relate to the total, such as showing the breakdown of a country’s budget.

Disadvantages of using proportional divided circles

1. Hard to Compare Multiple Circles: If you have more than one circle to compare, it becomes difficult to accurately compare the proportions across them, especially if the circles are not the same size.
2. Not Good for Large Datasets: Proportional divided circles are best for small datasets. If there are too many categories, the chart becomes cluttered and hard to interpret.
3. Limited Use for Complex Data: They work well for showing simple part-to-whole relationships but are not suitable for more complex datasets with multiple variables.
4. Hard to Read with Similar Sizes: It can be difficult to accurately read and compare sections that are very similar in size, especially if they are small portions of the circle.
5. Requires Accurate Labeling: Without clear labels, it can be confusing for students to understand what each section of the circle represents.

Divided semicirclesThese are half circle which are partitioned. There are two kinds of divided semicircles. These are,

1. simple divided semicircles
2. Proportional divided semicircles

Simple divided semicirclesThese are semi circular in nature but segmented accordingly. The segmentation are guided by 180 degree instead of 360 degrees as used in pie chart. ProceduresNote: The procedures are similar to that of drawing simple pie chart except the degrees are obtained by using 180 degree instead of 360 degrees. **Example.**by using the data tables above in proportional divided circles draw a simple divided semi-circle to represent number of lion hunted from 2009 to 2012. Trend of some of the wild animals hunted From 2009 to 2012 in degrees

Year	Species
	Elephant	Lion	Leopard	Hippopotamus	Buffalo
2012	$\frac{41}{211} \times 360^\circ = 70^\circ$	$\frac{37}{211} \times 360^\circ = 63^\circ$	$\frac{40}{211} \times 360^\circ = 68^\circ$	$\frac{40}{211} \times 360^\circ = 68^\circ$	$\frac{53}{211} \times 360^\circ = 90^\circ$
2011	$\frac{45}{201} \times 360^\circ = 81^\circ$	$\frac{27}{201} \times 360^\circ = 48^\circ$	$\frac{44}{201} \times 360^\circ = 79^\circ$	$\frac{38}{201} \times 360^\circ = 68^\circ$	$\frac{47}{201} \times 360^\circ = 84^\circ$

2010	$\frac{96}{1665} \times 360^\circ = 21^\circ$	$\frac{98}{1665} \times 360^\circ = 21^\circ$	$\frac{205}{1665} \times 360^\circ = 44^\circ$	$\frac{158}{1665} \times 360^\circ = 34^\circ$	$\frac{1108}{1665} \times 360^\circ = 24^\circ$
2009	$\frac{98}{1681} \times 360^\circ = 21^\circ$	$\frac{120}{1681} \times 360^\circ = 26^\circ$	$\frac{249}{1681} \times 360^\circ = 53^\circ$	$\frac{153}{1681} \times 360^\circ = 33^\circ$	$\frac{1061}{1681} \times 360^\circ = 227^\circ$

Solution

Find the total of items $\text{Total} = 37 + 27 + 98 + 120$ $\text{Total} = 282$

To find radius $\sqrt{282}$ $= 16.79$

Scale: Let 1 cm represent 3 units(cm) Then, $\frac{16.79}{3} = 5.5 \text{ cm}$ Hence, radius = 5.5 cm

To find degree (180°) for each year $2012 = \frac{37}{282} \times 180^\circ = 23.61^\circ$ $2011 = \frac{27}{282} \times 180^\circ = 17.23^\circ$ $2010 = \frac{98}{282} \times 180^\circ = 62.55^\circ$ $2010 = \frac{120}{282} \times 180^\circ = 76.59^\circ$

Note: Draw a divided semicircle to segment them accordingly. The segment should be portioned in a clockwise direction as in simple pie charts. A simple divided semicircle representing number of lions hunted from 2009 to 2012

Advantages of using simple divided semicircle

1. Shows Proportions Clearly: Divided semicircles are good for showing how different parts contribute to a whole, making it easy for students to understand proportions.
2. Visually Simple: The semicircular shape is less overwhelming than a full circle and easier for students to interpret, especially for smaller datasets.
3. Useful for Part-to-Whole Relationships: They are effective for representing data where students need to see how parts relate to the total, like percentages of boys and girls in a school.
4. Easy to Draw: Compared to other types of graphs, a semicircle is simpler to draw accurately with basic tools.
5. Takes Up Less Space: Since it's half a circle, it can fit better in limited spaces, such as small sections of a worksheet or a presentation.

Disadvantages of using simple divided semicircle

1. Limited Data Capacity: Semicircles are only suitable for a small number of categories. Too many divisions can make it cluttered and hard to read.
2. Not Good for Comparisons: It’s challenging to compare multiple semicircles accurately, especially if their sizes differ.
3. Difficult to Interpret Similar Sections: If the sections are of similar size, it can be hard for students to distinguish between them visually.
4. Requires Accurate Labeling: Without clear labels and a key, students may struggle to understand what each section represents.
5. Not Suitable for Detailed Data: Simple divided semicircles are best for basic data and are not useful for complex datasets with multiple variables.

Proportional divided semicircle ProceduresThe following are procedures for construction of proportional divided semi-circles

1. Calculate the total of two semicircles given, let radii be represented by R1 and R2 ;
2. Find the radius of both totals by applying the square roots to the obtained total;
3. Determine the scale of each semicircle first, then divide the totals by scales to obtain two radii;
4. Use the two radii to determine the size of semi circles;
5. Express each semi-circle by percentage or degree (fraction of 360º) as in simple pie chart or proportional pie chart. It is recommended to follow either ascending or descending order;
6. Draw the divided semicircle; and
7. Write the title and key.

ExampleGypsum production and export in ‘000 tonnes in Tanzania from 2013 to2016

Year	Production ('000 tonnes)	Export ('000 tonnes)
2016	214	214
2015	255	225
2014	200	200
2013	281	172
Total	950	811

Solution

The radii of two circles are determined by:

$\text{Radius (R)} = \sqrt{T}$

Where; T = the total value of the given item Find the total of every item. The totality for the first item is 950 and the total for the second item is 811. Find the radius for both totals

$\text{R1} = \sqrt{950} = 30.82$

$\text{R2} = \sqrt{811} = 28.48$

Determine the scale for every item Scale: Let 1 cm represent 10 units (cm)

$30.82 \div 10 = 3.1 \text{ cm}$

$28.48 \div 10 = 2.8 \text{ cm}$

Calculate the degrees

Gypsum production and export in‘000 tonnes in Tanzania from 2013 to 2016 in degrees

Year	Production ('000 tonnes)	Export ('000 tonnes)
2016	$\frac{214}{950} \times 180^\circ = 41^\circ$	$\frac{214}{811} \times 180^\circ = 48^\circ$
2015	$\frac{255}{950} \times 180^\circ = 48^\circ$	$\frac{225}{811} \times 180^\circ = 50^\circ$
2014	$\frac{200}{950} \times 180^\circ = 38^\circ$	$\frac{200}{811} \times 180^\circ = 44^\circ$
2013	$\frac{281}{950} \times 180^\circ = 53^\circ$	$\frac{172}{811} \times 180^\circ = 38^\circ$

Draw a proportional divided semi-circle Gypsum production and export in Tanzania from 2013 to 2016

Advantages of using Proportional divided semicircle

1. Shows Proportions Clearly: Proportional divided semicircles help students easily understand how parts contribute to the total in a visually clear way.
2. Compact Representation: Since it uses half a circle, it takes up less space while still showing proportional relationships effectively.
3. Good for Comparing Two Halves: It’s ideal for data where students need to compare two main categories, like boys versus girls or profit versus expenses.
4. Visually Appealing: The semicircular shape is simple yet engaging, making it easier for students to focus on the key information.
5. Simpler to Draw than Full Circles: For practical exercises, proportional divided semicircles are easier for students to draw and label than full circles.

Disadvantages of using Proportional divided semicircle

1. Limited Data Capacity: Proportional divided semicircles are best for small datasets. Too many categories make them difficult to read and interpret.
2. Difficult to Compare Multiple Semicircles: Comparing proportions across different semicircles can be challenging, especially if their sizes differ.
3. Requires Accurate Labeling: Without proper labels and a key, students may not understand what each segment of the semicircle represents.
4. Hard to Interpret Similar Sections: If two or more sections are close in size, it can be hard to tell them apart, leading to confusion.
5. Not Ideal for Complex Data: Proportional divided semicircles are not suitable for data that needs to show detailed relationships or trends over time.