Draw a frequency polygon for the following frequency distribution.
$C I$ $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$ $70 - 80$
$f$ $12$ $18$ $6$ $10$ $8$ $25$ $22$ $4$

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Solution

Construct a histogram for the given data. Mark the mid point of the tops of rectangles of histogram and join these points by line segments. To complete the polygon, mark two classes $(- 10$ to $0)$ and $(80$ to $90)$ . Join the end point of the line segments to the mid points of these two classes. The curve so obtained is a frequency polygon.

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Class interval	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$
Frequency	$4$	$6$	$8$	$10$	$12$	$14$	$7$	$5$

Class interval	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$
Frequency	$4$	$6$	$8$	$10$	$12$	$14$	$7$	$5$

Marks	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
No. of Students	$12$	$22$	$35$	$40$	$60$	$52$	$40$	$30$	$5$

Marks	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$3$	$7$	$10$	$6$	$8$	$2$	$4$

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$C I$	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
$f$	$12$	$18$	$6$	$10$	$8$	$25$	$22$	$4$