Question

In the table given below, class-mark and frequencies are given. Construct the frequency table taking inclusive and exclusive classes.

Class width	Frequency
22	6
24	7
26	13
28	4

Answer 1

Suppose the lower limit of classes among 22 classes is x₁, and the upper limit is x₂.

Class mark = `("Lower class limit" + "Upper class limit")/2`

`22 = (x_1 + x_2)/2`

∴ x₁ + x₂ = 44    ...(1)

The difference between the classes of two adjacent classes is equal to the class width of each class.

∴ Class width = 24 − 22

= 26 − 24

= 2

∴ x₂ − x₁ = 2

∴ − x₁ + x₂ = 2 ...(2)

Solving equations (1) and (2) gives the values x₁ = 21 and x₂ = 23.

First-class = 21 − 23 hence next class are 23 − 25, 25 − 27 and 27 − 29.

So, the exclusive frequency table is given by:

Exclusive class	Class-mark	Frequency
21 − 23	22	6
23 − 25	24	7
25 − 27	26	13
27 − 29	28	4

Class width = Upper limit − Lower limit

= 23 − 21

= 2

Also, the inclusive frequency table is given by:

Inclusive class	Class-mark	Frequency
21.5 − 22.5	22	6
23.5 − 24.5	24	7
25.5 − 26.5	26	13
27.5 − 28.5	28	4