Question

The number of coins collected by Ram on 5 consecutive days are 2,4,6,8,10. Find the standard deviation using step deviation method.

• A. 2.42
• B. 3.45
• C. 3.89
• D. 4.25

Answer 1

The correct option is A 2.42

We know that the observations are divisible by 2.

Let Assumed mean, A = 6, n = 5.

$\begin{array}{cccc}xi& di=xi-A& di=\frac{xi-A}{c}& d{i}^2\\ & di=xi-6& c=2& \\ 2& -4& -2& 4\\ 4& -2& -1& 1\\ 6& 0& 0& 0\\ 8& 2& 1& 1\\ 10& 4& 2& 4\\ & & \sum di=0& \sum d{i}^2=10\end{array}$

Standard Deviation

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

$=\sqrt{\frac{10}{5}-0}\times 2=2\sqrt{2}=2.42$