Question

Find the median of the following data. 

Class interval	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	Total
Frequency	8	16	36	34	6	100

Answer 1

1. Construct cumulative frequency table

First, calculate the cumulative frequency (cf) for each class interval by adding each frequency sequentially to the previous sum:

Class Interval	Frequency (f)	Cumulative Frequency (cf)
0 – 10	8	8
10 – 20	16	24 (8 + 16)
20 – 30	36	60 (24 + 36)
30 – 40	34	94 (60 + 34)
40 – 50	6	100 (94 + 6)
Total	N = 100

2. Identify median class

The total number of observations is N = 100.

Find the position value:

`N/2 = 100/2 = 50`

The cumulative frequency just greater than or equal to 50 is 60, which corresponds to the class interval 20 – 30. Therefore 20 – 30 is our median class.

3. Apply median formula

The formula to calculate the median for grouped data is:

Median = `L + ((N/2 - cf_"prev")/f) xx h`

Extract the parameters from our median class:

L (Lower limit of the median class) = 20

cf_prev (Cumulative frequency of the preceding class) = 24

f (Frequency of the median class) = 36

h (Class width/size) = 10

Substitute these values into the formula:

Median = `20 + ((50 - 24)/36) xx 10`

Median = `20 + (26/36) xx 10`

Median = `20 + 260/36`

Median = 20 + 7.222...

Median ≈ 27.22

The median value of the grouped frequency distribution is exactly 27.22.