Draw a frequency polygon from the following data by using (i) histogram, and (ii) without using histogram:

Daily Wages (in ₹) 10−15 15−20 20−25 25−30 30−35

Number of Workers 40 70 60 80 60

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Solution

Using a histogram, a frequency polygon is obtained by joining the top mid-points of the rectangles of the histogram.

When frequency polygon is to be drawn without a histogram then, we simply plot the mid-points of the class intervals with their respective frequencies. The curve obtained on joining the points is the frequency polygon.

Daily Wages Mid Point No. of Workers

10 − 15 $\frac{10 + 15}{2} = 12.5$ 40

15 − 20 $\frac{10 + 15}{2} = 17.5$ 70

20 − 25 $\frac{10 + 15}{2} = 22.5$ 60

25 − 30 $\frac{10 + 15}{2} = 27.5$ 80

30 − 35 $\frac{10 + 15}{2} = 32.5$ 60

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Class	5-10	10-15	15-20	20-25	25-30
Frequency	20	30	50	40	10

Using a graph paper, draw an ogive for the following distribution, which shows daily wages of 160 workers.

Using the graph determine:

Variable	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	10	20	35	40	25	25	15

Marks Obtained	10−20	20−30	30−40	40−50	50−60	60−70
Number of Students	5	12	15	22	14	4

Marks Obtained	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Number of Students	10	16	20	20	22	15	8	5

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Daily Wages (in ₹)	10−15	15−20	20−25	25−30	30−35
Number of Workers	40	70	60	80	60