Question

The Goals scored by players in a game are given below.
$\begin{array}{ccccc}x& 3& 4& 5& 6\\ f& 2& 3& 4& 5\end{array}$
Find the standard deviation of their goals scored by assumed mean method.

• A. 1.059
• B. 2.212
• C. 2.314
• D. 4.215

Answer 1

The correct option is A 1.059

Let the Assumed mean, A = 4
$\begin{array}{ccccc}xi& fi& di=xi-A& fidi& fid{i}^2\\ 3& 2& -1& -2& 2\\ 4& 3& 0& 0& 0\\ 5& 4& 1& 4& 4\\ 6& 5& 2& 10& 20\\ & n=14& & \sum fidi=12& \sum fid{i}^2=26\end{array}$

Standard Deviation

$\sigma =\sqrt{\frac{\sum fid{i}^2}{N}-(\frac{\sum fidi}{N}{)}^2}$

$=\sqrt{\frac{26}{14}-(\frac{12}{14}{)}^2}\simeq 1.059$