Question

The amount that the children have spend on buying stickers are 5,10,15,20,25. Find the standard deviation using step deviation method.

• A. 7.07
• B. 3.28
• C. 8.08
• D. 5.75

Answer 1

The correct option is A 7.07

We know that the observation are divisible by 5.
Let Assumed mean, A = 15, n = 5.

$\begin{array}{cccc}xi& di=xi-A& di=\frac{xi-A}{c}& d{i}^2\\ & di=xi-15& c=5& \\ 5& -10& -2& 4\\ 10& -5& -1& 1\\ 15& 0& 0& 0\\ 20& 5& 1& 1\\ 25& 10& 2& 4\\ & & \sum di=0& \sum d{i}^2=10\end{array}$

Standard Deviation

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

$=\sqrt{\frac{10}{5}-0}\times 5=5\sqrt{2}\simeq 7.07$