The following is the distribution of ages (in years) of children in a group:

Age (in years)	10	7	4	6	3	8
No. of Children	11	3	6	4	9	5

What is the median age (in years) of children?

Formula used:

Median for discrete frequency distribution. First, calculate cumulative frequencies. If N (total frequency) is odd, median is the value corresponding to (N+1)/2^th observation. If N is even, median is the average of values corresponding to N/2^th and (N/2)+1^th observations.

Calculation:

Arrange the data in ascending order of age and find the cumulative frequencies (cf):

Age: 3, Frequency: 9, Cumulative Frequency: 9

Age: 4, Frequency: 6, Cumulative Frequency: 9 + 6 = 15

Age: 6, Frequency: 4, Cumulative Frequency: 15 + 4 = 19

Age: 7, Frequency: 3, Cumulative Frequency: 19 + 3 = 22

Age: 8, Frequency: 5, Cumulative Frequency: 22 + 5 = 27

Age: 10, Frequency: 11, Cumulative Frequency: 27 + 11 = 38

Total number of children (N) = 38

Since N is even, the median is the average of the N/2^th and (N/2)+1^th observations.

⇒ 38/2^th = 19^th observation

⇒ (38/2) + 1^th = 20^th observation

From the cumulative frequency:

The 19^th observation falls in the cumulative frequency 19, which corresponds to an age of 6 years.

The 20^th observation falls in the cumulative frequency 22, which corresponds to an age of 7 years.

Median = (6 + 7) / 2

⇒ Median = 13 / 2

⇒ Median = 6.5