The mean of the following frequency table is 10. Find the value of a.

$x_{i}$ $f_{i}$

10 10

12 5

14 a

15 2

5 8

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Solution

Calculating the arithmetic mean from the given frequency table:

$x_{i}$ $f_{i}$ $f_{i} x_{i}$

10 10 100

12 5 60

14 a 14a

15 2 30

5 8 40

$\sum f_{i}$ = 25 + a $\sum f_{i} x_{i}$ = 230 + 14a

Given, mean=10
$\Rightarrow$ mean= $\frac{\sum f_{i} x_{i}}{\sum f_{i}}$ = $\frac{230 + 14 a}{25 + a}$ =10
$\Rightarrow$ 230 + 14a = 250 + 10a
$\Rightarrow$ 4a = 20
$\Rightarrow$ a = 5

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