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The missing frequency from the following distribution, being given that the median of the distribution is 24 is 26. State true or false.

Age (in years)
Number of persons
0-10
5
10-20
25
20-30
X
30-40
18
40-50
7

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True

False

answer is B.

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Detailed Solution

Given:

Age (in years)	Number of persons
0-10	5
10-20	25
20-30	x
30-40	18
40-50	7

Median is a value of separating the higher half from the lower half of a data sample.
Formula used:

M = L + N 2 − F f C

,
where, L= lower class limit, N= number of values, F=cumulative frequency, f=frequency, C=group width.
Median of the data set is 24.
We have to find the value of x. The frequency table of the given data will be

Age (in years)	Number of persons	Cumulative Frequency (CF)
0-10	5	5
10-20	25	5+25=30
20-30	x	30+x
30-40	18	30+x+18=48+x
40-50	7	48+x+7=55+x

We know that

m = 24, L = 20, N = 55 + x, F = 30, f = x, C = 10

.
Calculating the value of x using the median formula:

24 = 20 + 55 + x 2 − 30 x 10 24 − 20 = 55 + x − 60 2 x 10 4 = x − 5 2 x 10 8 x = 10 x − 50 2 x = 50 x = 25

The value of x is 25.
Thus, the given statement is false so the correct option is 2.

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