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The median of the following data is 16. Find the missing frequencies A and B, if the total of the frequencies is $70$ .

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8

and

7

5

and

7

8

and

2

4

and

7

answer is A.

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Detailed Solution

Given is a table of frequencies, median is 16, total frequency is 70.
Question Image

Total frequency N = 70

Median

= 16

Writing the cumulative frequency table,
Question Image

∴ 15 - 20

is median class
Median

= L + \frac{\frac{N}{2} - cf}{f} \times h

Here,
L is lower limit of Median class.
h is Class interval is 5-0=5

c_{f} = cumulative frequency of class before median class = 24 + A

Frequency of median class =15
Now,
Median=L+

\frac{\frac{N}{2} - Cf}{f} \times h

\Rightarrow

16=15+

\frac{\frac{70}{2} - (24 + A)}{15} \times 5

\Rightarrow

16-15=

\frac{35 - 24 - A}{3}

\Rightarrow

\frac{11 - A}{3}

\Rightarrow

3=11-A

\Rightarrow

A=11-3

\Rightarrow

A=8
Now, calculating value of B,

\sum fi = 55 + A + B

\Rightarrow 70 = 55 + A + B

Substituting,

A = 8

\Rightarrow 70 = 55 + 8 + B

\Rightarrow 70 = 63 + B

\Rightarrow 70 - 63 = B

\Rightarrow B = 7

Thus, the missing value of A and B are

8

and

7

.
Therefore, option (1) is correct.

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