Question

A group of 50 items has mean & S.D. 61 and 8 respectively. Another group of 100 observations has mean and S.D. 70 & 9 respectively. Find the approximate value of S.D. of the combined group

Answer 1

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Answer 2

Given,

S.D. of 50 observations in first group = 61

Mean of 50 observations in first group = 8

S.D. of 100 observations in second group = 70

Mean of 100 observations in second group = 9

To Find,

The S.D. of  combined group.

Solution,

The standard deviation can be calculated as follows:

$S.D. = \sqrt{\frac{sum of(each reading-mean)^{2} }{Total number of population} }$

So for the first group,

$8^{2} =$ $\frac{sum of (x_{1} -61)^{2} }{50}$

⇒ 64×50 = $sum of (x_{1} -61)^{2}$ → Equation 1

Similarly, for the second group,

$9^{2}$ = $\frac{sum of (x_{2} -70)^{2} }{100}$

⇒ 81×100= ${sum of (x_{2} -70)^{2}$ → Equation 2

S.D. for the combined group = $\sqrt{\frac{sum of((x_{1}+x_{2}) -(61+70))^{2} }{150} }$

From → Equation 1 and Equation 2

⇒ $\sqrt\frac{((64)(50)+(81)(100)}{150}$

=8.68.

Henceforth, the S.D. of the combined group is 8.68.