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


 

Answers (1)

Answer. [48.4]

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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