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Maths-

General

Easy

Question

A frequency distribution has arithmetic mean 7.85, then missing term is

10 5
10 05
15 5
15

hint Hint:

We are given a frequency distribution. We are given the value of its arithmetic mean. We have to find the value of the missing term.

The correct answer is: 15

The formula of arithmetic mean is
$m space equals fraction numerator begin display style sum from i to n of end style x subscript i f subscript i over denominator N end fraction$
Here x_iis the quantity whose frequency we measure.
f is the frequency of that quantity.
N is sum of all the frequencies. Here it means total number of workers.
$stack sum x subscript i with i below and n on top f subscript i space end subscript equals 5 space cross times space 10 space plus space 6 space cross times space x space plus space 7 space cross times space 13 space plus space 10 space cross times space 8 space plus space 12 space cross times space 5 space plus space 15 space cross times space 4 space space space space space space space space space space space space equals space 50 space plus space 6 x space plus space 91 space plus space 80 space plus space 60 space plus space 60 space space space space space space space space space space space space equals space 341 space plus space 6 x$
N = 10 + x + 13 + 8 + 5 + 4
= 40 + x
We are given m = 7.85
Now, we will substitute all the values and find the answer.
$m space equals space fraction numerator begin display style stack sum f subscript i with i below and n on top end style x subscript i over denominator N end fraction 7.85 equals space fraction numerator 341 space plus space 6 x over denominator 40 space plus space x end fraction 7.85 left parenthesis 40 space plus space x right parenthesis space equals space 341 space plus space 6 x 314 space plus space 7.85 x space equals space 341 space plus space 6 x space space 7.85 x space minus space 6 x space equals space 341 space minus space 314 space space space space space space space space space space space 1.85 x space equals 27 D i v i d i n g space b o t h space t h e space s i d e s space b y space 1.85 space space space space space space space space space space space space space space x space equals space fraction numerator 27 over denominator 1.85 end fraction space space space space space space space space space space space space space space space space space space space space space equals space 14.59 space space space space space space space space space space space space space space space space space space space almost equal to 15 space space space space space space space space space space space space space space space$
So, the missing term is 15.

For such questions, we need the the formula for arithmetic mean.

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