1.

Find mean, median and mode for the following dataClass:-1-1011-2021-3031-4041-5051-6061-7071-8081-9091-100frequency:-37131712108866​

Answer»

Answer:

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=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

−f 2

f−f

1 ×h

⇒ Mode=60+

2×12−10−6

12−10

×20

⇒ Mode=60+5=65


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