The daily wages of 160 workers in a factory are given below :

Wages (in ₹)	No. of workers
50-60	12
60-70	20
70-80	30
80-90	38
90-100	24
100-110	16
110-120	12
120-130	8

Draw a cumulative frequency curve and estimate :

(i) median wage

(ii) inter-quartile range

(iii) percentage of workers who earn more than ₹ 95 per day.

Cumulative frequency distribution table :

(i) Here, n = 160, which is even.

By formula,

Median = $\dfrac{n}{2} = \dfrac{160}{2}$ = 80th term.

Steps of construction :

1. Take 2 cm along x-axis = 10 rupees.

2. Take 1 cm along y-axis = 20 workers.

3. Plot the point (50, 0) as ogive starts on x-axis representing lower limit of first class.

4. Plot the points (60, 12), (70, 32), (80, 62), (90, 100), (100, 124), (110, 140), (120, 152) and (130, 160).

5. Join the points by a free-hand curve.

6. Draw a line parallel to x-axis from point A (no. of workers) = 80, touching the graph at point F. From point F draw a line parallel to y-axis touching x-axis at point G.

From graph, G = 85

Hence, median = 85.

(ii) Here, n is even.

Lower quartile = $\dfrac{n}{4}\text{ th term} = \dfrac{160}{4}$ = 40th term.

Draw a line parallel to x-axis from point B (no. of workers) = 40, touching the graph at point J. From point J draw a line parallel to y-axis touching x-axis at point I.

From graph, I = 73

Lower quartile = 73.

Upper quartile = $\dfrac{3n}{4}\text{ th term} = \dfrac{3 \times 160}{4}$ = 120th term.

Draw a line parallel to x-axis from point C (no. of workers) = 120, touching the graph at point H. From point H draw a line parallel to y-axis touching x-axis at point K.

From graph, K = 98

Upper quartile = 98.

Inter quartile range = Upper quartile - Lower quartile

= 98 - 73 = 25.

Hence, inter-quartile range = 25.

(iii) Draw a line parallel to y-axis from point P (wage) = ₹ 95, touching the graph at point Q. From point Q draw a line parallel to x-axis touching y-axis at point R.

From graph, R = 112

∴ 112 workers earn less or equal to ₹ 95.

Workers earning more = 160 - 112 = 48.

Percentage of workers earning more = $\dfrac{48}{160} \times 100$ = 30%.

Hence, 30% of workers earn more than ₹ 95.