Question

2. The mode of the following frequency distribution of 165 observation is 38 :
class
5 - 14
14 - 23
23 - 32
32 - 41
41 - 50
50 - 59
frequency
8
13
a
53
b
18
12
Find the values of a and b.​

Answer 1

Step-by-step explanation:

Here, modal class =32−41

⇒ l=32,f

0

=a,f

1

=53,f

2

=b and h=9

⇒ Mode=l+

2f

1

−f

0

−f

2

f

1

−f

0

×h

⇒ 34.5=32+

2×53−a−b

53−a

×9

⇒

9

2.5

=

106−a−b

53−a

⇒ 265−2.5a−2.5b=477−9a

⇒ 7.5a−2.5b=212

⇒ 75a−25b=2120

∴ 13a−5b=424 ------ ( 1 )

As total observation are 165

⇒ So, 5+11+a+53+b+16+10=165

⇒ 95+a+b=165

∴ a+b=70 -------- ( 2 )

∴ b=70−a

Substitute b=70−a in equation ( 1 )

⇒ 13a−5(70−a)=424

⇒ 13a−350+5a=424

⇒ 18a=424+350

⇒ 18a=774

∴ a=43

⇒ b=70−43=27

∴ Frequency a=43 and b=27