Question:
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
Correct Option: 1
Solution:
Let $x$ be the $6^{\text {th }}$ observation
$\Rightarrow 45+54+41+57+43+x=48 \times 6=288$
$\Rightarrow x=48$
variance $=\left(\frac{\Sigma x_{i}^{2}}{6}-(\bar{x})^{2}\right)$
$\Rightarrow$ variance $=\frac{14024}{6}-(48)^{2}$
$=\frac{100}{3}$
$\Rightarrow$ standard deviation $=\frac{10}{\sqrt{3}}$
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