Question

Calculate Median value from the following frequency distribution:

X	3	5	7	9	11	13
Y(Frequency)	4	3	5	2	3	3

• A. 6.5
• B. 6
• C. 5.5
• D. 7

Answer 1

The correct option is D 7

In order to find the median of the grouped discrete data, first we find the cumulative frequencies and the sum of frequencies.

Find the cumulative frequencies by adding the nth frequency to the sum of all the n-1 frequencies before it.

X	Y (frequency)	Z (Cumulative Frequency)
3	4	4
5	3	7
7	5	12
9	2	14
11	3	17
13	3	20

$\sum f$ = 4+3+5+2+3+3 =20

Since N is even, the median is:

Median = $\frac{N+1}{2}$ th term

Therefore: $\frac{20+1}{2}$ = $\frac{21}{2}$ = $10.5$

The Median is the average of the 10th and 11th value of the data.

Since both, the 10th and 11th term is 7, the median of the data set is 7.