Find the mean,median and mode of the following data
Answers
Answer:
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Classes x
i
f
i
f
i
x
i
c.f
0−20 10 6 60 6
20−40 30 8 240 14
40−60 50 10 500 24
60−80 70 12 840 36
80−100 90 6 540 42
100−120 110 5 550 47
120−140 130 3 390 50
∑f
i
=50 ∑f
i
x
i
=3120
⇒ Mean=
∑f
i
∑f
i
x
i
=
50
3120
=62.4
⇒ N=50 and
2
N
=25
∴ Median class =60−80
l= lower limit of the modal class
h= size of the class intervals
f= frequency of the modal class
f
1
= frequency of the class preceding the modal class
f
2
= frequency of the class succeed in the modal class.
⇒ Here, l=60,f=12,cf=24,h=20
Median=l+
f
2
N
−cf
×h
⇒ Median=60+
12
25−24
×20
⇒ Median=60+
12
20
=61.66
⇒ Modalclass=60−80
⇒ l=30,f=12,f
1
=10,f
2
=6,h=20
Mode=l+
2f−f
1
−f
2
f−f
1
×h
⇒ Mode=60+
2×12−10−6
12−10
×20
⇒ Mode=60+5=65
