Question

If the mean of following distribution is 54 find the missing frequency

Class  0-20  20-40  40-60  60-80  80-100
Frequency  16  14  24  26   x

Answer 1

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Answer 2

Answer:

The value of the missing frequency is 20

Solution:

Note: The values given below are from the table attatched below.

Refer the image.

$x_{i}$ can be calculated by adding the given class and dividing the sum by 2.

For example, for the class 0-20,

$x_{i}=\frac{0+20}{2}=10$

$\Sigma f=16+14+24+26+x=80+x$

$\sum f i x i=160+420+1200+1820+90 x=3600+90 x$

Given,

$M e a n=\frac{\sum f_{i} x_{i}}{\sum f}=54$

$\frac{3600+90 x}{80+x}=54$

$3600+90 x=54(80+x)$

$3600+90 x=4320+54 x$

$90 x-54 x=4320-3600$

$36 x=720$

$x=20$

Hence, the missing frequency is 20.