the marks obtained by 20 students are as follows :- 4,6,5,9,3,2,7,7,6,5,4,9,10,10,3,4,7,6,9,9,. 1.)Find the mean , median and mode of the data. 2.) Find the total observation in the given data.
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Answer:
Marks Mid−value
x
i
No.offrequency
f
i
c.f f
i
x
i
0−10 5 1 1 5
10−20 15 4 5 60
20−30 25 5 10 125
30−40 35 8 18 280
40−50 45 2 20 90
∑f
i
=20 ∑f
i
x
i
=560
⇒ Mean(
x
)=
∑f
i
∑f
i
x
i
=
20
560
=28
⇒ Modal class =30−40
So, l=30,f
0
=5,f
1
=8,f
2
=2 and h=10
⇒ Mode=l+
2f
1
−f
0
−f
2
f
1
−f
0
×h
=30+
2×8−5−2
8−5
×10
=30+3.33
∴ Mode=33.33
⇒ Here, n=20, then
2
n
=
2
20
=10
∴ Median class =20−30
So, c.f=5,f=5,l=20 and h=10
⇒ Median=l+
f
2
N
−c.f
×h
=20+
5
10−5
×10
=20+10
∴ Median=30
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