Question

 Find standard deviation for the following data:

X 6 9 12 15 18

f 7 12 13 10 8

Answer 1

To find the standard deviation let us take $A$( assumed mean) $=12$ . Then calculate the following table such as

Now the formula for standard deviation is $\sigma =\sqrt{\frac{\Sigma f.d^2}{N}-(\frac{\Sigma f.d}{N})^2}$ where $N=\Sigma f$

From the above table we get , $\sigma =\sqrt{\frac{738}{50}-(\frac {0}{50})^2}$ $=\sqrt{14.76}\approx 3.84$ (correct upto two decimal places)

Therefore required standard deviation is $=3.84$ (approximately)