Question

prepare a less than cumulative frequency distribution hence find no of students having marks below 20​

Answer 1

Step-by-step explanation:

10th

Maths

Statistics

Mean of Grouped Data

Find the mean marks of the ...

STATISTICS

Find the mean marks of the students from the following cumulative frequency distribution:

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

Number of students: 5 9 17 29 45 60 70 78 83 85

MEDIUM

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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 u

i

10

x

i

−55

f

i

u

i

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

Total N=∑f

i

=85 ∑f

i

u

i

=−56

We have,

N=N=∑f

i

=85,∑f

i

u

i

=−56,h=10andA=55

∴

X

=A+h(

N

1

∑f

i

u

i

)

⇒

X

=55+10×

85

−56

=55−6.59=48.41Marks.

Hence, mean marks scored by the students = 48.41.

Answered By abdulrehman