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The following frequency distribution is classified according to the number of mangoes in different branches. What is the median of the mangoes in each branch?

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37.68

36.87

38.76

25.83

answer is D.

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Detailed Solution

It is given a following frequency distribution which is classified according to the number of mangoes in different branches.
Question Image

We create a cumulative frequency table for the given data as shown below:

Number of mangoes	Branch(f)	Cumulative frequency
0 - 10	5	5
10 - 20	4	9
20 -30	6	15
30 - 40	2	17
40 - 50	4	21
50 - 60	3	24
60 - 70	1	25

We know that,

Median = l + (\frac{\frac{n}{2} - cf}{f}) \times h

From the table, we get

n = 25

So,

\frac{n}{2} = \frac{25}{2}

\Rightarrow \frac{n}{2} = 12.5

, which is nearest to

15

(cumulative frequency)
We get that the observation lies in the class

20 - 30

So, we get

l = 20, cf = 9, f = 6, h = 10

Putting the values in the formula, we get

\Rightarrow Median = 20 + (\frac{12.5 - 9}{6}) \times 10

\Rightarrow Median = 20 + \frac{3.5}{6} \times 10

\Rightarrow Median = 20 + \frac{35}{6}

\Rightarrow Median = 20 + 5.83

\Rightarrow Median = 25.83

Thus, the median of the data is 25.83.
Hence, the correct option is 4.

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