Ways of Presenting Statistical Data

There are various types of bar and line graphs used to present geographical data. The main bar and line graphs include:

1. Simple bar and line graphs
2. Grouped bar and line graphs
3. Compound bar and line graphs
4. Divergent bar and line graph

Line graphs have unique properties that distinguish them from other graphs. The properties of line graphs are as follows:

1. The graphs are drawn by plotting a dependent variable against an independent variable and points are joined by a line.

2. The values on the y-axis start at point zero.

General procedures for drawing line graphs

1. Get the required data for plotting the graph.
2. Identify the independent and dependent variable. Statistically, the independent variables are placed on the x-axis while the dependent variables are placed on the y-axis.
3. Decide on the vertical scale depending on the graph space and values of the independent variable available.
4. Decide on the horizontal spacing of the graph according to graph space available.
5. Draw and divide the vertical and horizontal axes depending on the respective scales.
6. Plot and join the points to get the graph.
7. Write the title of the graph you have drawn.
8. Indicate the scale of the graph.
9. Show the key for the graph if need be.

Line graphs can be sub-divided into:

1. Simple line graphs
2. Group (comparative) line graphs
3. Compound line graphs
4. Divergent line graphs

Presenting the statistical data by a simple line graph is the most common and popular method. The simple line graphs are easy to construct and interpret. They have many uses which include showing temperature, farm outputs, population, and mineral production, among others.

The following procedures may be used

1. Identify the variables. The dependent variable is temperature and the independent variable is months.
2. Determine a vertical scale. Assume that the graph space available is 6 cm vertically. Vertical scale = maximum value of the divided by the graph space available e.g. 30°C/6 cm = 5°C per centimeter. Therefore, in the vertical axis (x-axis), 1 cm will represent 5°C
3. Determine the horizontal scale (y-axis) depending on the available space. Let, for instance, 1 cm represent one month.
4. Draw both axes and label them: y-axis for temperature and x-axis for months.
5. Plot the points and join them by a smooth line to make a curve.
6. Insert the title and scale.

The following table which shows the average monthly temperature recorded in a certain weather station:

Average monthly temperature for station

Scale

Vertical – 1 cm:5°C

Horizontal – 1 cm:1 month

Advantages of simple line graphs

1. They are easy to draw, read and interpret.
2. They show specific values of data, so if you are given one variable the other can easily be determined.
3. They show patterns in data clearly, meaning that they visibly show how one variable is affected by the other as it increases of decreases.
4. They enable the viewer to make predictions about the results of data. So they allow for determination of intermediate or continuing values.
5. It is easy to read the exact values against plotted points on straight line graphs.
6. A broken scale can be used when the value starts at a large number.

Disadvantages of simple line graphs

1. They can only be used to show the data of one item over time.
2. One can change the data of a line graph by not using consistent scales on the axis.
3. They can give a wrong impression on the continuity of data even when there are periods when data is not available.
4. They do not give a clear visual impression of the actual quantities.

A group line graph is also known by the following terms:

1. Comparative line graph
2. Composite line graph
3. Multiple line graph
4. Polygraph

A group line graph involves drawing more than one line on the same statistical graph. It shows the relationship between sets of similar statistics for two or more items.

Usefulness of a group line graph

i. Comparing different values or trends in two or more data variables.

ii. Examining the possibility of a relationship existing between the distributions of a number of variables over time.

iii. Comparing the distribution of the same variable at different places.

The following things should be considered before drawing the graph

1. The lines drawn should not be uniform in color, thickness, general appearance, etc (See the graph below in which each line has a different color).
2. The number of lines that a graph can accommodate should not exceed 5, meaning that not more than 5 items should be compared in a single graph.

The following table shows banana production (in tonnes) by three villages in Ingwe Division, Tarime district. These data have been used to plot the group (comparative) line graph as shown below:

Banana production by three villages

Solution

Scale

H. Scale

1cm represent 1 year

V. Scale

1cm represent 5 tonne("00")

GROUP LINE GRAPH SHOWING BANANA PRODUCTION BY THREE VILLAGES BETWEEN 2000 AND 2002

Advantages of group line graph

1. The quantity of each component is shown clearly by different line shadings.
2. Time and space are saved since all the line graphs are drawn at ago as a group.

Disadvantages of group line graph

1. The lines can be overcrowded and hence become difficult to read and interpret if many data are involved.
2. It does not give a clear visual impression of actual quantities.

A compound line graph is used to analyze the total and the individual inputs of the specific commodities or economic sectors. The graph involves drawing two or more lines, each line corresponding to one item in a different year or region. The items are differentiated from each other or one another by shading differently.

The table below is used for construction of the graph. The table contains hypothetical figures for mineral exports between 2010 and 2012.

Procedure

1. Simplify the data to make the presentation work easy by dividing each value by 1000.

Add the values for each year to get the cumulative export:

2010 = 10+16+20 = 46

2011 = 20+25+32 = 77

2012 = 25+35+40 =100

These values will be used to determine the uppermost height of the graph. They will also help estimate the scale to be used. In case of the above data, the highest value is 100. So if we want to use the scale of 1 cm to 1 tonne (1000 tonnes in reality), the uppermost height of our graph will be 100 cm (see the graph drawn)

Plot the values for mineral exports against years on a graph. Usually the line graph for data with the highest values is drawn first. Thus, first draw the line graph for tanzanite since it has the highest values, followed by that of gold and finally diamond

Draw the second line graph above the first one to show the next component. To get the values for plotting the second line graph, add the values of the first item (in this case, tanzanite) to that of the second item (gold) for each year, thus:

2010 = 20+6 =36

2011 = 32+25 =57

2012 = 40+35 =75

Draw the line graph for the last item (diamond) above that of the second item. To get the values for plotting this graph, add the values for the second item to those of the last item, thus:

2010 = 36+10 =46

2011 = 57+20 =67

2012 = 75+25 =100

1. Shade the component parts between the line graphs using different shadings as shown.
2. Label the axes, show the key and indicate the scale used to construct the graph.

Scale

H.scale 2cm represent 1year

COMPOUND LINE GRAPH MINERAL EXPORTS BETWEEN 2010 AND 2012

Advantages of compound line graph

1. Total values are shown clearly and easily.
2. It gives good visual impression.
3. Combining all graphs in one saves time and space.

Disadvantages of compound line graph

1. Graph construction is difficult and time-consuming.
2. It involves a lot of calculations which are difficult and time-consuming.
3. It is difficult to read and interpret the value for any one commodity for any particular year.

A divergent line graph is a line graph which shows how variables deviate from the mean. The mean is represented by zero axis drawn horizontally across the graph paper.

In the give data draw the divergent line graph to present the data given.

Construction

Step we calculate mean

$\sum X/N$

where

Σ X = Summation of the value

N = number of items/ Occurrence value

Sum up the values of all items or commodities. 1000 + 1500 + 500 + 3000 = 6000

1. Calculate the arithmetic mean (average) of the values. 6000/4 = 1500 Thus the arithmetic mean = 1500
2. Calculate the deviation from the mean of each value as shown in the table below.

Deviation from the mean value

Plot the graph using the values of deviation from the mean; and remember to include the title and scale of the graph.

DIVERGENT LINE GRAPH SHOWING THE PRODUCTION OF COMMODITIES

Advantages of divergent line graph

1. It clearly shows how items fluctuate from the mean.
2. It compares the values of the items and hence facilitates a sound conclusion.
3. It shows both the positive (profit) and negative (loss) phenomena.
4. It is easy to construct, read and interpret.

Disadvantages of divergent line graph

1. It involves many calculations and hence time-consuming.
2. It might be difficult to interpret if one lacks statistical skills.
3. It is applicable for only one item per graph.

A bar graph is also called bar chart or columnar graph. This method is used to present data which are not continuous. This means that in a bar graph there is no relationship between or among data.

Types of bar graphs

1. Simple bar graphs
2. Group or comparative bar graphs
3. Compound bar graphs
4. Divergent bar graphs

A simple bar graph is drawn to show a single item per bar. It mainly represents simple data.

Construction

1. Choose the appropriate scale. However, note that the table below is not drawn to scale – it was drawn using the computer. All hand-drawn graphs must indicate the scale used. For, example, in our graph below, we might have chosen 1 cm to represent 10,000 tones, in which case we could obtain the values 5, 10, 15, 20 and 25 that we could have used to plot the graph.
2. Draw the axes and insert the bars. Note that all the bars must have the same width and spacing.
3. Shade the bars uniformly by using shade, lines, crosses, dots, etc.
4. Insert vertical and horizontal scales and the title.

Consider the data in the table below which shows the value of sisal exported by Tanzania between 1900 and 1994:

Solution

Scale: 1 cm to 50,000 tonnes

H. Scale: 1 cm to 1 year

SIMPLE BAR GRAPH SHOWING TANZANIA SISAL EXPORT FROM 1900 AND 1994

Advantages of a simple bar graph

1. It is simple to construct, read and interpret.
2. It has a good visual impression.
3. It can be used to compare how the amount of an item varies from time to time.

Disadvantages of a simple bar graph

1. It is limited to only one item or commodity and hence not suitable for massive data.
2. Not suitable for continuous data such as temperature.

A comparative/group bar graph consists of several bars drawn side by side on the same chart for the purpose of comparison. The technique involves grouping of bars in a chart. The graph can be used to show how production of certain commodities varies each year.

The procedure for construction of the comparative bar graph is similar to that of drawing the simple bar graph except that the simple bar graph contains a single bar while the comparative bar graph comprises of multiple bars.

Consider the data in the table below, showing agricultural production in metric tonnes.

GROUP (COMPARATIVE) BAR GRAPH SHOWING CROP YIELDS IN '000 KG (1986 - 1988)

Advantages of a group bar graph

1. The total values are expressed well for illustration of points.
2. It is easy to construct, read and interpret.
3. The importance of each component is shown clearly.

Disadvantages of a group bar graph

1. It is difficult to compare the totals of each item/component.
2. Trends such as fall and rise cannot be shown easily.

Compound/divided bar graph is a method of data presentation that involves construction of bars which are divided into segments to show both the individual and cumulative values of items. The length of each segment represents the contribution of an individual item in the total length while that of the whole bar represents the total (cumulative) value of items in each group.

Construction

For example, consider the table below, which shows the number of tourists who visited the named Tanzania National Parks from 1998 to 2002.

How to construct the compound bar graph

1. Simplify the data (to make the presentation work easy) by dividing each value by 10,000. Then add the values to get the total for each year. The simplified data are as shown in the table below.
2. Determine the scale of the bar length based on the highest total value. In this case, the highest total value is 68 (20 + 20 + 10 + 18). Recall the construction of the compound line graph! If we choose 1 cm to represent 1 tourist (10,000 tourists in reality), then the length of the tallest bar will be 68 cm. Note that the maximum height of a graph for each year equals the cumulative total values for each year (i.e. 43, 46, 48, 59, 68).
3. Decide on the bar spacing, for example, 2 cm apart.
4. Draw the axes and label them.
5. Start by drawing bars that represent the highest values.
6. The first sets of bars to be drawn are those that represent the highest values. On top of these, the second highest segments are drawn. The last segments to be drawn are those with the lowest values in general.
7. To make it easy to follow the rise and fall of individual values, a soft line could be drawn across bars to separate individual segments.
8. Colour or shade the segments to improve the appearance and simplify interpretation.
9. Inset the scales, key and title.

COMPOUND (DIVIDED) BAR GRAPHS SHOWING TOURIST VISITS IN 0'000 (1998 - 2002)

Advantages of compound (divided) bar graph

1. It is easy to read and interpret as the totals are clearly shown.
2. It gives a clear visual impression of the total values.
3. It clearly shows the rise and fall in the grand total values.

Disadvantages of compound (divided) bar graph

1. The values of individual segments above the first set are difficult to establish because they don't start at zero. To get the correct values of the top segments, you have to add the figures, which is difficult for someone not well equipped with statistical skills.
2. The graph is very difficult to construct and interpret.
3. It is not easy to represent a large number of components as this would involve very long bars with many segments.

A divergent bar graph is a graph which shows the increase or decrease of value.

Construction

1. Calculate the arithmetic mean (average) of the items.
2. Subtract the mean from each item.
3. Draw the graph using the resulting values.
4. Insert the scale and title of the graph.

The data below show the enrolment of Form One students at Mara Secondary School from 1980–1985. Study the table and present the data by a divergent bar graph.

Find the arithmetic mean:

Subtract the mean from each item:

Choose a suitable scale and construct the graph using the obtained values (X – ).

DIVERGENT BAR GRAPH SHOWING STUDENT ENROLLMENT (1980-1985)

Advantages of divergent bar graph

1. Fluctuation in values, which helps to detect the problem in general terms, is shown.
2. It is important for comparison of positives and negatives.
3. Profit (success) or loss (failure) can easily be deduced.
4. They are simple to construct, read and interpret.

Disadvantages of divergent bar graph

1. Graph construction is time-consuming since it involves many steps.
2. The calculations involved may be difficult to someone who is poor at mathematics.
3. It is limited to analysis of only one variable.

A divided circle is also known as pie chart, circle chart or pie graph. The chart involves dividing the circle into "pie slices" to represent and show relative sizes of data. The size of each slice or segment is always proportional to the value it represents. Divided circles can appear in two forms:

1. Simple divided circles.
2. Proportional divided circles.

A simple divided circle involves a single set of data whereas the proportional divided circle involves more than one set of data such that the circles will be proportional to the total quantity that each circle represents.

Construction

Obtain the data to work on. Study this hypothetical record showing enrollment of Form One students in selected Secondary Schools in Monduli District:

A table showing student enrollment in selected schools in Monduli District

1. Calculate the total number of students as shown in the table.
2. Calculate the angle in a circle that would represent the number of students enrolled in each school. For example, 85 out of 456 students enrolled in Nyansincha Secondary School will be represented in the circle by a segment with an angle of 85/456 ×630 = 67 degrees.This will give the following results:

1. Draw a circle of a reasonable size.
2. Using a protractor, draw a radius from the 6 o'clock mark to the centre of the circle.
3. Starting with the largest segment representing a specific component, measure and draw its angle from the centre of the circle.
4. Do the same for other components in ascending order.
5. Divide a circle into segments according to the sizes of the angles.
6. Shade the segments and write the title and key of the drawn graph.

PIE CHART/DIVIDED CIRCLE SHOWING STUDENT ENROLLMENT IN SELECTED SECONDARY SCHOOLS IN MONDULI DISTRICT

Advantages of divided circles

1. It is easy to compare components as they are represented by angles.
2. Analysis and interpretation of data is easy.
3. It is easy to assess the proportion of individual components against the total.
4. Construction of this graphical representation is relatively simple.
5. It is easy to determine the value of each component since it is indicated on each segment.
6. Visual impression of the individual components is clear and facilitates the understanding of the information in the data.

Disadvantages of divided circles

1. It is time-consuming because it involves a lot of calculations.
2. The represented actual values remain hidden as the values shown on the faces of the segments may be in percentages.
3. Where the range of data is large and involves small and big values, accurate construction of the chart is difficult.
4. When the values of data set vary slightly, it is difficult to visualize the proportional differences between values (as it is the case in the pie chart above).