Draw a frequency polygon imposed on the histogram for the following distribution.
Class interval $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$ $70 - 80$ $80 - 90$
Frequency $4$ $6$ $8$ $10$ $12$ $14$ $7$ $5$

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Solution

Take the class-intervals along the X-axis and frequencies along the Y-axis with appropriate scale as shown.
Now mark the mid points of the upper sides of the consecutive rectangles. We also make the midpoints of the assumed class intervals $0 - 10$ and $90 - 100$ . The mid points are joined with the help of a ruler. The ends of the polygon are joined with the mid points of $0 - 10$ and $90 - 100$ . Now, we get the 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	$4$	$6$	$8$	$10$	$12$	$14$	$7$	$5$

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

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

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

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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