Question

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

Class width	Frequency
5	3
15	9
25	15
35	13

Answer 1

Suppose, the lower limit of the  5 classes is x₁ and the upper limit is x₂.

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

5 = `(x_1 + x_2)/2`

∴ x₁ + x₂ = 10   ...(1)

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

∴ class width = 15 − 5 = 25 − 15 = 10

∴ x₂ + x₁ = 10

∴ − x₁ + x₂ = 10   ...(2)

Let's sum the equations (1) and (2).

      x₁ + x₂ = 10
+ − x₁ + x₂ = 10
___________________
           2x₂ = 20

∴ x₂ = 10

The value of x₂ = 10 is put into equation (1)

x₁ + 10 = 10

∴ x₁ = 10 − 10

∴ x₁ = 0

∴ First-class = 0 − 10. From this the next class are 10 − 20, 20 − 30 and 30 − 40.

So, the exclusive frequency table is given by:

Exclusive class	Classmark	Frequency
0 − 10	5	3
10 − 20	15	9
20 − 30	25	15
30 − 40	35	13

class width = Upper limit − Lower limit

= 10 − 0 = 10

Also, the inclusive frequency table is given by:

Inclusive class	Classmark	Frequency
0.5 − 9.5	5	3
10.5 − 19.5	15	9
20.5 − 29.5	25	15
30.5 − 39.5	35	13