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}}

 

Answers (1)

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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