Question

If mode of the following frequency distribution is 31, then find the value of p
Class
5-15
15 - 25
25 - 35
35 - 45
45 - 55
15
11
6
Frequency
3
р

Answer 1

Answer:

Let us first consider the value of b.

It is given that a : b = 2 : 3 and b : c = 4 : 5. Thus, LCM of 3 and 4 is 12. Therefore, we need to multiply the first ratio by 4 and the second ratio by 3.

⇒⇒ a : b = 4(2) : 4(3) = 8 : 12

⇒⇒ b : c = 3(4) : 3(5) = 12 : 15

Now, as the value of b is common across the two ratios, we can combine them.

Therefore, a : b : c = 8 : 12 : 15.

Now, we shall make the value of c common.

The ratios with us are a : b : c = 8 : 12 : 15 and c : d = 6 : 7.

LCM of 15 and 6 is 30. Therefore, we need to multiply the first ratio by 2 and the second ratio by 5.

⇒⇒ a : b : c = 2(8) : 2(12) : 2(15) = 16 : 24 : 30

⇒⇒ c : d = 5(6) : 5(7) = 30 : 35

Now, as the value of c is common across the two ratios, we can combine them.

Therefore a : b : c : d = 16 : 24 : 30 : 35

Answer 2

Answer:

The class 35-45 has maximum frequency. Therefore, this is the modal class.

l=35,h=‘10,f=23,f

1

=21,f

2

=14

Therefore,

Mode = l+

2f−f

1

−f

2

f−f

1

×h

=35+

46−21−14

23−21

×10

=35+

11

2

×10

=35+

11

20

=36.81