Question

The number of televisions sold in each day of a week are 13, 8, 4, 9, 7, 12, 10. Find it's standard deviation by direct method.

• A. 2.83
• B. 3.87
• C. 4.52
• D. 6.35

Answer 1

The correct option is A 2.83

$\begin{array}{cc}xi& x{i}^2\\ 13& 169\\ 8& 64\\ 4& 16\\ 9& 81\\ 7& 49\\ 12& 144\\ 10& 100\\ \sum xi=63& \sum x{i}^2=623\end{array}$

Standard Deviation

$\sigma =\sqrt{\frac{\sum x{i}^2}{n}-(\frac{\sum xi}{n}{)}^2}$

$=\sqrt{\frac{623}{7}-(\frac{63}{7}{)}^2}$

$=\sqrt{89-81}=\sqrt{8}$

$\sigma \simeq 2.83$