Draw a frequency polygon for the following data using histogram.
Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
Number of students 5 4 6 8 5 7 4 9 5 7

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Solution

Mark the class intervals along the X-axis and the number of students along the Y-axis. Draw a histogram for the given data. Now mark the mid points of the upper sides of the consecutive rectangles. The mid points are joined with the help of a ruler. Note that, the first and last edges of the frequency polygon meet at the mid point of the vertical edges of the first and last rectangles.

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Class-interval:	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency:	5	8	7	12	28	20	10	10

C.I	10-30	30-50	50-70	70-90	90-110	110-130	130-150
f	4	7	5	9	5	6	4

Marks	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Number of students	5	4	6	8	5	7	4	9	5	7

Class	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90
Frequency	9	11	15	24	19	9	8	5

Class Interval	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	12	20	26	18	10	6

Sales in Rs. thousand	40-50	50-60	60-70	70-80	80-90	90-100
Number of Companies	5	15	25	30	20	5