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Question

A student scores the following marks in five test: $$45, 54, 41, 57, 43$$. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six test is 


A
103
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B
1003
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C
1303
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D
103
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Solution

The correct option is D $$\dfrac{10}{\sqrt{3}}$$
Let $$x$$ be the $$6^{th}$$ observation
$$\Rightarrow 45 + 54 + 41 + 57 + 43 + x = 48 \times 6 = 288$$
$$\Rightarrow x = 48$$
Variance $$= \left(\dfrac{\sum x_i^2}{6} - (\bar{X})^2\right)$$
$$\Rightarrow$$ variance $$=\dfrac{14024}{6} - (48)^2$$
$$=\dfrac{100}{3}$$
$$\Rightarrow$$ standard deviation $$=\dfrac{10}{\sqrt{3}}$$

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