Question

Calculate the median (briefly explain how you solved this problem in your written work)

X f

5     1​

4     2

3     3

1 4

0 2

​

Answer 1

First we will total all the frequency to find if number of observations are odd or even.

Total frequency = 1 + 2 + 3 + 4 + 2 = 12

For odd number of observations, median is at (n+1)/2 position.

For even number of observations, the median is at the mid point or average of n/2 and n/2 + 1 positions.

n/2 position = 12 / 2 = 6th position

n/2 +1 position = 12/2 + 1 = 7th position

To find the right value as median, we need to sort the X column in ascending order.

X 0 1 3 4 5

f 2 4 3 2 1

Now X = 0 has 2

X = 1 = 2 + 4 = 6 (3rd to 6th position are 1, hence, 6th position is 1)

X = 3 = 6 + 3 = 9 (7th to 9th position are 3, hence, 7th position is 3)

Median is the average of 6th and 7th position values = (1 + 3) / 2 = 4 / 2 = 2

Hence, the Median is 2