Directions:

Study the following table carefully and answer the questions that follow:

Age (in years)	Number of employees (Frequency)	Cumulative frequency
30 - 35	5	5
35 - 40	7	12
40 - 45	6	18
45 - 50	9	27
50 - 55	4	31

Based on above table, answer the following questions:

17. The total number of employees is :

(a) 30
(b) 31
(c) 55
(d) Cannot be determined

18. How many employees are less than 50 years of age?

(a) 9
(b) 18
(c) 27
(d) 31

19. How many employees are atleast 40 years old?

(a) 12
(b) 18
(c) 19
(d) 27

20. What is the difference between the class-mark of the first and last class intervals?

(a) 20
(b) 22.5
(c) 25
(d) 27.5

17. The total number of employees in a frequency distribution is the sum of all individual frequencies, which is equal to the cumulative frequency of the last class interval.

∴ The total number of employees is 31.

Hence, Option (b) is the correct option.

18. As we know,

In a grouped data of exclusive form, the data related to upper limit is excluded.

Given, frequency distribution are 30 - 35, 35 - 40, 40 - 45, 45 - 50.

Since, number of employees less than 50 years of age corresponds to the cumulative frequency for the class 45 - 50 = 27.

Hence, Option (c) is the correct option.

19. Given, atleast 40 years old,

The classes includes, 40 - 45, 45 - 50 and 50 - 55.

Frequency of classes = 6 + 9 + 4 = 19

Hence, Option (c) is the correct option.

20. We know that,

Class mark = $\dfrac{\text{Upper limit + Lower limit}}{2} = \dfrac{48 + \text{U}}{2}$

Class mark of first class = $\dfrac{30 + 35}{2} = \dfrac{65}{2}$ = 32.5

Class mark of last class = $\dfrac{50 + 55}{2} = \dfrac{105}{2}$ = 52.5

Difference = 52.5 - 32.5 = 20

Hence, Option (a) is the correct option.