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

Engineering

Mathematics

Measure of Central Tendency

Question

$\frac{10}{3}$

$\frac{100}{3}$

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

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

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$AM = \frac{41 + 45 + 54 + 57 + 43 + x}{6} = 48$

⇒ x = 48

$σ^{2} + 48^{2} = \frac{1}{6} (41^{2} + 45^{2} + 54^{2} + 57^{2} + 43^{2} + 48^{2})$

$σ^{2} = \frac{14024}{6} - 2304 = \frac{100}{3}$