Question

Find the standard deviation for the following data:
$\begin{array}{cccccc}{x}_i& 3& 8& 13& 18& 23\\ f_i& 7& 10& 15& 10& 6\end{array}$

• A. 5.37
• B. 15.92
• C. 6.12
• D. 13.87

Answer 1

The correct option is C 6.12

Applying assumed mean method to calculate the standard deviation, and assuming the mean to be 0 we get:
$\begin{array}{ccccc}{x}_i& f_i& f_i{x}_i& x_i^2& f_i{x}_i^2\\ 3& 7& 21& 9& 63\\ 8& 10& 80& 64& 640\\ 13& 15& 195& 169& 2535\\ 18& 10& 180& 324& 3240\\ 23& 6& 138& 529& 3174\\ Total& 48& 614& & 9652\end{array}$
Now, $\sigma =\frac{1}{N}\sqrt{N\sum f_i{x}_i^2-{(\sum f_i{x}_i)}^2}=\frac{1}{48}\sqrt{48\times 9652-(614{)}^2}=\frac{1}{48}\times 293.77=6.12$