Question

52. 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 59-68
13
8
a
53
18
b
12
Frequency
Find the values of a and b.

Please give a swer if you can solve it ​

Answer 1

Answer:

Here, modal class

=

32

−

41

⇒

l

=

32

,

f

0

=

a

,

f

1

=

53

,

f

2

=

b

and

h

=

9

⇒

M

o

d

e

=

l

+

f

1

−

f

0

2

f

1

−

f

0

−

f

2

×

h

⇒

34.5

=

32

+

53

−

a

2

×

53

−

a

−

b

×

9

⇒

2.5

9

=

53

−

a

106

−

a

−

b

⇒

265

−

2.5

a

−

2.5

b

=

477

−

9

a

⇒

7.5

a

−

2.5

b

=

212

⇒

75

a

−

25

b

=

2120

∴

13

a

−

5

b

=

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 )

⇒

13

a

−

5

(

70

−

a

)

=

424

⇒

13

a

−

350

+

5

a

=

424

⇒

18

a

=

424

+

350

⇒

18

a

=

774

∴

a

=

43

⇒

b

=

70

−

43

=

27

∴

Frequency

a

=

43

and

b

=

27