Question

The marks scored by the students in a test are given below.
$\begin{array}{cccccc}x& 4& 6& 8& 10& 12\\ f& 7& 3& 5& 9& 5\end{array}$
Find the standard deviation of their marks by assumed mean method.

• A. 5.22
• B. 3.91
• C. 2.87
• D. 4.48

Answer 1

The correct option is C 2.87

Let the assumed mean, A = 8
$\begin{array}{ccccc}xi& fi& di=xi-A& fidi& fid{i}^2\\ 4& 7& -4& -28& 112\\ 6& 3& -2& -6& 12\\ 8& 5& 0& 0& 0\\ 10& 9& 2& 18& 36\\ 12& 5& 4& 20& 80\\ & n=29& & \sum fidi=4& \sum fid{i}^2=240\end{array}$

Standard Deviation

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

$=\sqrt{\frac{240}{29}-(\frac{4}{29}{)}^2}=\sqrt{\frac{6944}{29\times 29}}$

$\Rightarrow 6\simeq 2.87$