Find the mean of each of the following frequency distributions :

The given series is an inclusive series. Firstly, make it an exclusive series.

Let the assumed mean be A = 42 and h = 5.

We know that mean, $\bar{X}=A+h\left(\frac{1}{N} \sum f_{i} u_{i}\right)$

Now, we have $N=\sum f_{i}=70, \sum f_{i} u_{i}=-79, h=5$ and $A=42$.

Putting the values in the above formula, we have

$\bar{X}=A+h\left(\frac{1}{N} \sum f_{i} u_{i}\right)$

$=42+5\left(\frac{1}{70} \times(-79)\right)$

$=42-\frac{395}{70}$

$=42-5.6438$

$=36.3571$

Hence, the mean is 36.357.