Question

The following tables gives the frequency distribution of number of peas per pea pod of 198 pods:

Number of peas	1	2	3	4	5	6	7
Frequency	4	33	76	50	26	8	1

What is the median of this distribution?
1. 3
2. 4
3. 5
4. 6

Answer 1

Correct Answer - Option 1 : 3

Concept:

Median of 'n' observations is the value at the central position when the data is arranged in ascending or descending order.

• For, odd n, median is the value at the \(\rm \left(\frac{n+1}{2}\right)\) position.
• For even n, median is the mean of values at \(\rm \left(\frac{n}{2}\right)\) and \(\rm \left(\frac{n}{2}+1\right)\) position.

 

Calculation:

Writing the cumulative frequencies, we get

Number of peas	1	2	3	4	5	6	7
Frequency	4	33	76	50	26	8	1
Cumulative Frequency	4	37	113	163	189	197	198

 

Since n = 198 is even, the median will be the mean of the values at \(\rm \left(\frac{198}{2}\right)\) = 99^th position and 99 + 1 = 100^th position.

From the above table, both the 99^th and 100^th values are 3.

Therefore, the median of the above data is 3.