The number of observations in a group is 40. If the average of first 10 is 4.5 and that of the remaining 30 is 3.5 then the average of the whole group is

A
$\frac{15}{4}$
B
$\frac{1}{5}$
C
8
D
4

Solution:

We have,

$n_{1} = 10, n_{2} = 30, {\bar{X}}_{1} = 45, {\bar{X}}_{2} = 35$

Let 9 be the average of the whole group. Then

$\bar{X} = \frac{n_{1} {\bar{X}}_{1} + n_{2} {\bar{X}}_{2}}{n_{1} + n_{2}} = \frac{10 \times 45 + 30 \times 35}{40} = \frac{45 + 105}{40} = \frac{15}{4}$

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