Question

write the proper data and frequency and also find the median.

0 and above 80
10 and above 77
20 and above 72
30 and above 65
40 and above 55
50 and above 43
60 and above 28
70 and above 16
80 and above 10
90 and above 8
100 and above 0

Answer 1

Step-by-step explanation:

Here we have, the cumulative frequency distribution. So, first we convert it into an ordinary frequency distribution. we observe that are 80 students getting marks greater than or equal to 0 and 77 students have secured 10 and more marks. Therefore, the number of students getting marks between 0 and 10 is 80-77= 3.

Similarly, the number of students getting marks between 10 and 20 is 77-72= 5 and so on. Thus, we obtain the following frequency distribution.

Marks Number of students

0-10 3

10-20 5

20-30 7

30-40 10

40-50 12

50-60 15

60-70 12

70-80 6

80-90 2

90-100 8

Now, we compute mean arithmetic mean by taking 55 as the assumed mean.

Computative of Mean

Marks

(x

i

) Mid-value (f

i

) Frequency u

i

10

x

i

−55

f

i

u

i

0-10 5 3 -5 -15

10-20 15 5 -4 -20

20-30 25 7 -3 -21

30-40 35 10 -2 -20

40-50 45 12 -1 -20

50-60 55 15 0 0

60-70 65 12 1 12

70-80 75 6 2 12

80-90 85 2 3 6

90-100 95 8 4 32

Total

∑f

i

=80 ∑f

i

u

i

= -26

We have,

N= sumf

i

=80,∑f

i

u

i

=−26, A= 55 and h= 10

∴

X

=A+h[

N

1

∑f

i

u

i

]

⇒

X

=A+h[

N

1

∑f

i

u

i

]

⇒

X

=55+10×

80

−26

=55−3.25=51.75Marks.