Question

Calculate the mean and standard deviation for the following data:

Neck circumference

(in inches)

12 12.5 13 13.5 14 14.5 15 15.5 16

Frequency

5 20 30 43 60 56 37 16 3

Answer 1

To find the mean and standard deviation we will calculate the following table,

Here $A=$ assumed mean $=14$

Now the formula for mean is, $\bar x = A+ \frac{\Sigma fd}{\Sigma f}$

$=14+\frac{3.5}{270}=14.0129$

$\therefore$ The required mean is $=14.0129$

Again the formula for standard deviation is , $\sigma =\sqrt{\frac {\Sigma fd^2}{\Sigma f}-(\frac {\Sigma fd}{\Sigma f})^2}$

$=\sqrt{\frac {204.75}{270}-(\frac {3.5}{270})^2}$

$=0.8707$

$\therefore$ The required standard deviation is $=0.8707$