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Q.

The mean of marks obtained in an examination by a group of 100 students was found to be 49.96. The mean of the marks obtained in the same examination by another group of 200 students was 52.32, then the mean of the marks obtained by both the groups of students taken together is

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a

53

b

52

c

52.5

d

51.5

answer is A.

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Detailed Solution

$\bar{x} = \frac{n_{1} {\bar{x}}_{1} + n_{2} {\bar{x}}_{2}}{n_{1} + n_{2}}$

$n_{1} = 100, n_{2} = 100, \bar{x_{1}} = 49.96, \bar{x_{2}} = 52.32$

$\bar{x} = \frac{n_{1} {\bar{x}}_{1} + n_{2} {\bar{x}}_{2}}{n_{1} + n_{2}} = \frac{100 (49.96) + 200 (52.32)}{300} = 51.5$

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The mean of marks obtained in an examination by a group of 100 students was found to be 49.96. The mean of the marks obtained in the same examination by another group of 200 students was 52.32, then the mean of the marks obtained by both the groups of students taken together is