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The marks obtained by 20 students in tist were
12,13,0,0,1, 1,14,13, 12, 16, L1,9,6, 17, 21, 22,00
Find the mean marks per student.
(i) If extra smarks are given to each student, show
that mean marks also increased by s.
(iii) If a marks are deducted from each students,
show that the mean marks are also reduced by 2.
(iv) If marks of each student be dousted, then show
that the mean marks are also doubled.
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Answers
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.
Step-by-step explanation: