Question:
Find the mean of each of the following frequency distributions :
Solution:
Let the assumed mean be A = 20 and h = 8.
We know that mean, $\bar{X}=A+h\left(\frac{1}{N} \sum f_{i} u_{i}\right)$
Now, we have $N=\sum f_{i}=20, \sum f_{i} u_{i}=-9, h=8$ and $A=20$.
Putting the values in the above formula, we get
$\bar{X}=A+h\left(\frac{1}{N} \sum f_{i} u_{i}\right)$
$=20+8\left(\frac{1}{20} \times(-9)\right)$
$=20-\frac{72}{20}$
$=20-3.6$
$=16.4$
Hence, the mean is 16.4.