10 is the mean of a set of 7 observations and 5 is the mean of a set of 2 observations, the mean of the combined set is

10 is the mean of a set of 7 observations and 5 is the mean of a set of 2 observations, the mean of the combined set is

A
15
B
10
C
8.5
D
none of these

Solution:

We have

$n_{1} = 7, {\bar{X}}_{1} = 10, n_{2} = 3$ and ${\bar{X}}_{2} = 5$

Let $X$ be the Mean of the combined set. Then,

$\bar{X} = \frac{n_{1} {\bar{X}}_{1} + n_{2} {\bar{X}}_{2}}{m_{1} + n_{2}} = \frac{7 \times 10 + 3 \times 5}{7 + 3} = 8.5$

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