Question

Practice Questions
Quelis from the following dala compute the mean
the mean marks
of all the studenti of so schools in luty
Marks obtained More than or
30-35 25-30 20-25 15-20 less thanks
equal to 35
No
school
8
4
7.
9
15
5
250
300 200 150
Average No of student: 200
[And 27.85
10​

Answer 1

Answer:

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.