Question

Find the arithmetic mean of the following frequency distribution

Marks below
70
90
100
80
40
60
50
30
20
10
No. of students
115
104
86
109
97
50
70
22
35
12
​

Answer 1

Answer:

Here we have, cumulative frequency distribution less than type. First we convert it into an ordinary frequency distribution. We observe that the number of students getting marks less than 10 is 5 and 9 students have secured marks less than 20. Therefore,  number of students getting marks between 10 and 20 ( inclusive 0 and exclusive 10) is 9−5=4. Similarly, the number of students getting marks between 20 and 30 is 17−9=8 and so on. Thus, we have the following distribution frequency distribution:

Marks:  0−10  10−20  20−30   30−40  40−50  50−60  60−70  70−80  80−90  90−100

Number of students:   5     4      8       12       16      15     10       8       5       2

Let us Let us now compute arithmetic mean by taking 55 and the assumed mean.

Computation of Mean

Marks Mid-value Frequency

​  

 

0−10  5 5 −5 −25

10−20  10 4 −4 −16

20−30   25 8 −3 −24

30−40  35 12 −2 −24

40−50  45 16 −1 −16

50−60  55 15  0 0

60−70  65 10  1 10

70−80  75 8  2 16

80−90  85 5  3 15

90−100  95 2  4 8

Step-by-step explanation:

Hence, mean marks scored by the students = 48.41

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