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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

1 Answer

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Best answer
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

Cumulative Frequency 4 37 113 163 189 197 198

 

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

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

Therefore, the median of the above data is 3.

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