Question

Use graph paper for this question.
The table given below shows the monthly wages of some factory workers.
(i) Using the table, calculate the cumulative frequency of workers.
(ii) Draw the cumulative frequency curve.
Use 2 cm = ₹500, starting the origin at ₹6,500 on X-axis, and 2 cm = 100 worker at they Y-axis.
(iii) Use your graph to write down the median wages in ₹.

Wages in ₹ (CLass)	No. of workers (frequency)	Cumulative frequency f(x)
6500 - 7000	10	-
7000 - 7500	18	-
7500 - 8000	22	-
8000 - 8500	25	-
8500 - 9000	17	-
9000 - 9500	10	-
9500 - 10000	8	-

Answer 1

(i)

Wages in ₹ (CLass)	No. of workers (frequency)	Cumulative frequency f(x)
6500 - 7000	10	10
7000 - 7500	18	28
7500 - 8000	22	50
8000 - 8500	25	75
8500 - 9000	17	92
9000 - 9500	10	102
9500 - 10000	8	110

(ii) Plot the points (6500, 0), (7000, 10), (7500, 28), (8000, 75), (9000, 92), (9500, 102), (10000, 110) and join them by a free hand curve.

(iii) Here, N = 110
To find the median we shall construct a horizontal line at cumulative frequency
= `"N"/(2) = (110)/(2)` = 55,
intersecting the ogive at (8100, 55)
Hence, median wages = ₹8100.