Question

The following data represents the daily wages in rupees of a certain number of employees of a company:

Daily wages (in ₹)	No. of Employees
30 – 40	8
40 – 50	14
50 – 60	12
60 – 70	17
70 – 80	20
80 – 90	26
90 – 100	13
100 – 110	10

Use a graph to answer the following questions: 

1. Represent the above distribution by an ogive.
2. Find the following on the graph drawn:
   1. median wage.
   2. percentage of employees who earn more than ₹ 84 per day.
   3. number of employees who earn ₹ 56 and below.

Answer 1

Cumulative frequency distribution table:

Daily wages (in ₹)	No. of employees	Cumulative frequency
30 – 40	8	8
40 – 50	14	22
50 – 60	12	34
60 – 70	17	51
70 – 80	20	71
80 – 90	26	97
90 – 100	13	110
100 – 110	10	120

Here, n = 120, which is even.

Median = `n/2`

= `120/2`

= 60th term

Steps of construction:

1. Plot daily wages on x-axis.

2. Plot cumulative frequency on y-axis.

3. Mark points (40, 8), (50, 22), (60, 34), (70, 51), (80, 71), (90, 97), (100, 110) and (110, 120).

4. Draw a free hand curve passing through the points marked, strating from the lower limit of first class and terminating at upper limit of the last class.

5. Mark A = 60 on y-axis, draw a horizontal line which meets curve at B.

6. Through point B, draw a vertical line which meets x-axis at point C. The value of point C on x-axis is the median.

∴ Median wage is ₹ 74.

7. Mark D = 84 on x-axis, draw a vertical line which meets curve at E.

8. Through point E, draw a horizontal line which meets y-axis at point F. The value of point F on y-axis represents no. of employees earning less than or equal to ₹ 84 per day.

From graph,

F = 81.

No. of employees earning more than ₹ 84 per day

= 120 – 81

= 39

Percentage of employees earning more than ₹ 84

= `("No. of employees earining more than" ₹ 84)/"Total employees" xx 100`

= `39/120 xx 100`

= `3900/120`

= 32.5%

9. Mark G = 56 on x-axis, draw a vertical line which meets curve at H.

10. Through point H, draw a horizontal line which meets y-axis at point I. The value of point I on y-axis represents no. of employees earning less than or equal to ₹ 56 per day.

From graph,

I = 30.

No. of employees earning less than or equal to ₹ 56 per day = 30.