Median

In situations where one or more values are much higher or lower than the rest (called rogue values), the mean may not give a good representation of the average. In such cases, the median is a better measure of central tendency.

The median is the middle value when the data is arranged in order. If there is an odd number of values, the median is the middle one. If there is an even number of values, the median is the mean of the two middle values.

Example: Comparing median and mean

Mr. Samwel owns a small factory and earns 4,000,000/- per year. He employs 4 workers who earn:

550,000/-, 500,000/-, 450,000/-, and 400,000/-

Let's find the mean income:

Total income = 4,000,000 + 550,000 + 500,000 + 450,000 + 400,000 = 5,900,000/- Number of people = 5 Mean = 5,900,000 ÷ 5 = 1,180,000/-

If we tell one of the workers they earn about 1,180,000/-, they will disagree—because the employer's income is much higher than theirs. This is a case where the mean is misleading.

Now let's find the median:

Step 1: Arrange incomes in order

400,000, 450,000, 500,000, 550,000, 4,000,000

Step 2: Find the middle value

Median = 500,000/-

So the median gives a better idea of what most employees earn.

Example 1

Find the median of the numbers:

12, 23, 10, 8, 22, 14, 30, 18

Solution:

Step 1: Arrange in order

8, 10, 12, 14, 18, 22, 23, 30

Step 2: Since there are 8 numbers (even), take the average of the 4th and 5th values:

Median = (14 + 18) ÷ 2 = 32 ÷ 2 = 16

Example 2

Juma rolled a six-sided die 50 times. The results are shown below:

Score (x)	Frequency (f)
1	8
2	10
3	7
4	12
5	6
6	7
Total	50

Solution:

We are looking for the median position:

Since there are 50 scores, the median will be the average of the 25th and 26th items.

Let's find where the 25th and 26th scores fall by calculating cumulative frequency:

• 1 → 8
• 2 → 8 + 10 = 18
• 3 → 18 + 7 = 25
• 4 → 25 + 12 = 37

So:

• The 25th score is a 3
• The 26th score is a 4

Median = (3 + 4) ÷ 2 = 3.5