#### Find the mean age of 100 residents of a town from the following data : Age equal and above (in years) 0 10 20 30 40 50 60 70 Number of Persons 100 90 75 50 25 15 5 0

Solution. Here we calculate mean by following the given steps:

1. Find the mid point of each interval.
2. Multiply the frequency of each interval by its mid point.
3. Get the sum of all the frequencies (f) and sum of all the (fx)
4. Now divide sum of (fx) by sum of (f)

 Marks xi fi 0-10 5 100-90 =10 50 10-20 15 90-75 = 15 225 20-30 25 75-50 = 25 625 30-40 35 50-25 =25 875 40-50 45 25-15 =10 450 50-60 55 15-5 = 10 550 60-70 65 5-0 = 5 325 $\sum f_{i}= 100$ $\sum f_{i}x_{i}= 3100$

$mean\left ( \bar{x} \right )= \frac{\sum f_{i}x_{i}}{\sum f_{i}}= \frac{3100}{100}= 31$