The daily wages of 80 workers in a project are given below.

Wages (in ₹)	No. of workers
400 - 450	2
450 - 500	6
500 - 550	12
550 - 600	18
600 - 650	24
650 - 700	13
700 - 750	5

Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = ₹ 50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate :

(i) the median wages of the workers.

(ii) the lower quartile wage of workers.

(iii) the number of workers who earn more than ₹ 625 daily.

Cumulative frequency distribution table :

Here, n = 80, which is even.

Median = $\dfrac{n}{2}$ th term

= $\dfrac{80}{2}$ = 40th term.

(i) Steps of construction :

1. Take 2 cm = ₹ 50 on x-axis.

2. Take 1 cm = 10 workers on y-axis.

3. Plot the point (400, 0) as ogive starts on x-axis representing lower limit of first class.

4. Plot the points (450, 2), (500, 8), (550, 20), (600, 38), (650, 62), (700, 75) and (750, 80).

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

6. Draw a line parallel to x-axis from point I (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 K.

From graph, K = ₹ 605

Hence, median = ₹ 605.

(ii) Here, n = 80, which is even.

By formula,

Lower quartile = $\dfrac{n}{4} = \dfrac{80}{4}$ = 20th term.

Draw a line parallel to x-axis from point L (no. of workers) = 20, touching the graph at point Q. From point Q draw a line parallel to y-axis touching x-axis at point M.

From graph, M = ₹ 550

Hence, lower quartile = ₹ 550.

(iii) Draw a line parallel to y-axis from point N (wages) = ₹ 625, touching the graph at point O. From point O draw a line parallel to x-axis touching y-axis at point P.

From graph, P = 50.

∴ 50 workers earns either less or equal to ₹ 625.

Workers earning more than ₹ 625 = 80 - 50 = 30.

Hence, no. of workers earning more than ₹ 625 = 30.