A student scored the following marks in five | vedclass

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(D) Let the score of the sixth test be $x$. The mean of the six tests is given by: $\frac{45 + 54 + 41 + 57 + 43 + x}{6} = 48$ $240 + x = 288$ $x = 48

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) Let the score of the sixth test be $x$. The mean of the six tests is given by: $\frac{45 + 54 + 41 + 57 + 43 + x}{6} = 48$ $240 + x = 288$ $x = 48$ Now,the six scores are $41, 43, 45, 48, 54, 57$. The variance $\sigma^2$ is calculated as: $\sigma^2 = \frac{1}{n} \sum x_i^2 - (\bar{x})^2$ $\sigma^2 = \frac{41^2 + 43^2 + 45^2 + 48^2 + 54^2 + 57^2}{6} - 48^2$ $\sigma^2 = \frac{1681 + 1849 + 2025 + 2304 + 2916 + 3249}{6} - 2304$ $\sigma^2 = \frac{14024}{6} - 2304 = \frac{7012}{3} - \frac{6912}{3} = \frac{100}{3}$ Therefore,the standard deviation $\sigma = \sqrt{\frac{100}{3}} = \frac{10}{\sqrt{3}}$.

$A$ student scored 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 the six tests is:

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