Question

The marks scored by 5 students in a class are 25, 30, 35, 40 and 45. Find the standard deviation using Assumed mean method.

• A. 7.07
• B. 3.21
• C. 8.12
• D. 6.12

Answer 1

The correct option is A 7.07

The mean of the marks = 35
Hence, we take assumed mean, A = 35.
$\begin{array}{ccc}xi& di=xi-A& d{i}^2\\ & =xi-35& \\ 25& -10& 100\\ 30& -5& 25\\ 35& 0& 0\\ 40& 5& 25\\ 45& 10& 100\\ & \sum di=0& \sum d{i}^2=250\end{array}$.

Standard Deviation

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

$=\sqrt{\frac{250}{5}-\frac{0}{5}}=\sqrt{50}\simeq 7.07$