calulate mean of the following distribution
marks more than: 0 10 20 30 40 50 60 70 80 90 100
no. of studant:80 77 72 65 55 43 28 16 10 8 0
Answers
Explanation:
ANSWER
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.