Question

The number of cars manufactured in each day of a week are 2, 4, 6, 8, 10, 5, 7. Find the standard deviation of the number of cars manufactured using Direct method.

• A. 2.83
• B. 3.45
• C. 6.35
• D. 8.23

Answer 1

The correct option is A 2.83

$\begin{array}{cc}xi& x{i}^2\\ 2& 4\\ 4& 66\\ 6& 36\\ 8& 64\\ 10& 100\\ 5& 25\\ 7& 49\\ \sum xi=42& \sum x{i}^2=294\end{array}$

Standard Deviation

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

$=\sqrt{\frac{294}{7}-(\frac{42}{7}{)}^2}$

$=\sqrt{42-36}=\sqrt{8}\simeq 2.83$