# Determine the mean of the following distribution :   Marks Number of students Below 10 Below 20 Below 30 Below 40 Below 50 Below 60 Below 70 Below 80 Below 90 Below 100 5 9 17 29 45 60 70 78 83 85

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 cf fi fixi 0-10 5 5 5 15 10-20 15 9 9-5 =4 75 20-30 25 17 17-9 = 8 175 30-40 35 29 29-17 = 12 350 40-50 45 45 45-29 = 16 540 50-60 55 60 60-45 = 15 825 60-70 65 70 70-60 = 10 780 70-80 75 78 78-70 = 8 450 80-90 85 83 83-78 = 5 170 90-100 95 85 85-83 = 2 760 $\sum f_{i}= 85$ $\sum f_{i}x_{i}= 4115$

$mean\left ( \bar{x} \right )= \frac{\sum f_{i}x_{i}}{\sum f_{i}}= \frac{4115}{85}= 48\cdot 4$

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