Question:
Find the mean of each of the following frequency distributions :
Solution:
Let the assumed mean be A = 60 and h = 20.
We know that mean, $\bar{X}=A+h\left(\frac{1}{N} \sum f_{i} u_{i}\right)$
Now, we have $N=\sum f_{i}=50, \sum f_{i} u_{i}=14, h=20$ and $A=60$.
Putting the values in the above formula, we have
$\bar{X}=A+h\left(\frac{1}{N} \sum f_{i} u_{i}\right)$
$=60+20\left(\frac{1}{50} \times(14)\right)$
$=60+\frac{280}{50}$
$=60+5.6$
$=65.6$
Hence, the mean is 65.6.