# A student scores the following marks in five tests : 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 tests is: Option 1) $\frac{10}{\sqrt{3}}$ Option 2) $\frac{100}{3}$ Option 3) $\frac{10}{3}$ Option 4) $\frac{100}{\sqrt{3}}$

Let score of 6th test be x

then, $\frac{45+54+41+57+43+x}{6}=48$

x=48

$\sigma ^{2}=\frac{\sum \left ( x_{i} - \overline{x} \right )^{2}}{n}$

$\sigma ^{2}=\frac{3^{2}+6^{2}+7^{2}+9^{2}+5^{2}+0^{2}}{6}=\frac{200}{6}=\frac{100}{3}$

$\sigma ^{2}=\frac{100}{3}\Rightarrow \sigma =\frac{10}{\sqrt{3}}$

correct option (i)

Option 1)

$\frac{10}{\sqrt{3}}$

Option 2)

$\frac{100}{3}$

Option 3)

$\frac{10}{3}$

Option 4)

$\frac{100}{\sqrt{3}}$

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