Question

The scores of 8 students in a test are 16, 13, 21, 14, 9, 19, 24, 25. Find the standard deviation of their scores using direct method.

• A. 3.8
• B. 5.24
• C. 6.06
• D. 7.12

Answer 1

The correct option is B 5.24

$\begin{array}{cc}X& X^2\\ 16& 256\\ 13& 169\\ 21& 441\\ 14& 196\\ 9& 81\\ 19& 361\\ 24& 576\\ 25& 625\\ \sum X=141& \sum X^2=2705\end{array}$

$Mean,\overline{X}=\frac{\sum X}{N}=\frac{141}{8}=17.62$

$\sigma =\sqrt{\frac{\sum X^2}{N}-{\overline{X}}^2}=\sqrt{\frac{2705}{8}-{17.62}^2}=\sqrt{338.12-310.46}=\sqrt{27.48}=5.24$