Question

The table given below shows the frequency distribution of the monthly wages of the employees of a company:

Wages (in ₹)	400 – 499	500 – 599	600 – 699	700 – 799	800 – 899
No. of employees	12	17	13	8	3

Use this table and find: 

1. The lower limit of the fourth class; 
2. The upper limit of the fifth class; 
3. The class boundaries of second class; 
4. The class mark of first class; 
5. The class-size of third class.

Answer 1

Given: Table of wages and frequencies:

400 – 499 : 12

500 – 599 : 17

600 – 699 : 13

700 – 799 : 8

800 – 899 : 5

Step-wise calculation:

i. Lower limit of the fourth class:

Fourth class = 700 – 799

Lower limit = 700 the stated lower class limit.

ii. Upper limit of the fifth class:

Fifth class = 800 – 899

Upper limit = 899 the stated upper class limit.

iii. Class boundaries of the second class:

Second class (stated limits) = 500 – 599

Convert to continuous boundaries by subtracting/adding 0.5:

Lower boundary

= 500 – 0.5

= 499.5

Upper boundary

= 599 + 0.5

= 599.5

So, class boundaries = 499.5 – 599.5.

iv. Class mark of the first class:

First class = 400 – 499

Class mark = `(400 + 499)/2`

= `899/2`

= 449.5

v. Class-size of the third class:

Third class = 600 – 699 true boundaries 599.5 – 699.5

Class-size = 699.5 – 599.5 = 100

Equivalently, 699 – 600 + 1 = 100 for inclusive discrete classes.