Question

The marks obtained by 10 students are 43,48,55,57,42,50,47,48,58,50 then what is the standard deviation

Answer 1

Dear student
$$\begin{gathered} \mathrm{Mean}\left(\overline{\mathrm{x}}\right)=\frac{43+48+55+57+42+50+47+48+58+50}{10} \\ =49.8 \\ \mathrm{Variance}\left({\mathrm{\sigma }}^2\right)=\frac{{\displaystyle \sum _{}^{}}{\left({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{x}}\right)}^2}{\mathrm{n}} \\ =\frac{46.24+3.24+27.04+51.84+60.84+0.04+7.84+1.96+67.24+0.04}{10} \\ =26.632 \\ \mathrm{Standard}\mathrm{deviation}=\sqrt{\left({\mathrm{\sigma }}^2\right)}=5.160 \end{gathered}$$
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