Question

The frequency distribution of weights (in kg) of 40 persons is given below.

Weights (in kg)
30 - 35
35 - 40
40 - 45
45 - 50
50 - 55
Frequency
6
13
14
4
3
(a) What is the lower limit of fourth-class interval?
(b) What is the class size of each class interval?
(c ) Which class interval has the highest frequency?
(d) Find the class marks of all the class intervals?

Answer 1

Answer: (a) 4

(b) 5

(c) 14

(d)

Class interval Class mark

30 - 35
`(35+30)/(2)=32.5`

35 - 40
`(35+40)/(2)=37.5`

40 - 45
`(40+45)/(2)=42.5`

45 - 50
`(45+50)/(2)=47.5`

50 - 55
`(50+55)/(2)=52.5`

Explanation:

The data of 40 persons is given as :

Weights (in kg) Frequency

30 - 35 6

35 - 40 13

40 - 45 14

45 - 50 4

50 - 55 3

(a)

Lower limit is the lowest number in a class interval .

So, is the lower limit of fourth-class interval (45 - 50) is 4.

(b)

Class size = Upper limit - lower limit

So, Class size of first class interval = 35-30=5

Thus , class size of each interval is 5. [ class size remains same]

(c)

Highest frequency in table = 14 which is corresponding to 40 - 45 .

Thus , 40 - 45 is the class interval has the highest frequency.

(d)

Class mark is the mid value of each class interval.

Class interval =
`\frac{(\text{Upper limit+Lower limit})}{2}`

Class interval Class mark

30 - 35
`(35+30)/(2)=32.5`

35 - 40
`(35+40)/(2)=37.5`

40 - 45
`(40+45)/(2)=42.5`

45 - 50
`(45+50)/(2)=47.5`

50 - 55
`(50+55)/(2)=52.5`