The median is the middle value when the data is arranged in order from smallest to largest.

Steps to find the median:

1. Arrange all values in order (ascending)
2. Find the middle position
3. If there is an odd number of values, the median is the middle one
4. If there is an even number of values, the median is the average of the two middle values

Worked Example

The scores obtained by 7 pupils in a Mathematics test are: 45, 52, 38, 60, 55, 48, 41

1. Arrange in order: 38, 41, 45, 48, 52, 55, 60
2. There are 7 values (odd number)
3. The middle position is the 4th value: 48
4. Median = 48

Worked Example (Even number of values)

Weights of 6 bags of maize (in kg): 12, 15, 11, 14, 13, 16

1. Arrange in order: 11, 12, 13, 14, 15, 16
2. There are 6 values (even number)
3. The two middle positions are the 3rd and 4th values: 13 and 14
4. Median = (13 + 14) ÷ 2 = 27 ÷ 2 = 13.5 kg

The mode is the value that appears most often in the data set.

Steps to find the mode:

1. Look at each value and count how many times it appears
2. The value that appears most frequently is the mode
3. A data set may have no mode, one mode, or more than one mode

Worked Example

The number of books read by pupils in a month: 3, 5, 2, 5, 4, 5, 3, 2, 5

Counting the frequency:

• 2 appears 2 times
• 3 appears 2 times
• 4 appears 1 time
• 5 appears 4 times

The number 5 appears most frequently, so Mode = 5 books

The following data shows the prices of tomatoes (in Tanzanian shillings) at a market over 8 days: 2000, 2500, 1800, 2500, 2200, 2500, 1900, 2100

Mean: Sum = 2000 + 2500 + 1800 + 2500 + 2200 + 2500 + 1900 + 2100 = 17,500 Number of values = 8 Mean = 17,500 ÷ 8 = 2,187.5 TZS

Median: Arrange in order: 1800, 1900, 2000, 2100, 2200, 2500, 2500, 2500 Two middle values are 2100 and 2200 Median = (2100 + 2200) ÷ 2 = 2150 TZS

Mode: The value 2500 appears 3 times (most frequent) Mode = 2500 TZS

• Mean uses all values and gives the arithmetic average
• Median is the middle value and is not affected by extreme values
• Mode is the only measure that can be a non-number (categorical data)

In Tanzania, shopkeepers and farmers use mean, median, and mode to make daily decisions. For example, a vendor at Mwalimu Nyerere Market in Dar es Salaam might record how many kilograms of onions she sells each day for a week, then find the mean to know the average sales, the median to understand a typical day's sales, and the mode to know which quantity sells most often. This helps them plan how much stock to buy and set fair prices.