Question

Draw a frequency polygon for the following frequency distribution.

Class interval	1−10	11−20	21−30	31−40	41−50	51−60
Frequency	8	3	6	12	2	7

Answer 1

Though the given frequency table is in inclusive form, class marks in case of inclusive and exclusive forms are the same.
We take the imagined classes ($-$9)–0 at the beginning and 61–70 at the end, each with frequency zero.
Thus, we have:

Class Interval	Class Mark	Frequency
$-$9–0	–4.5	0
1–10	5.5	8
11–20	15.5	3
21–30	25.5	6
31–40	35.5	12
41–50	45.5	2
51–60	55.5	7
61–70	65.5	0

Along the x-axis, we mark –4.5, 5.5, 15.5, 25.5, 35.5, 45.5, 55.5 and 65.5.
Along the y-axis, we mark 0, 8, 3, 6, 12, 2, 7 and 0.
We have chosen the scale as follows :
On the x-axis, 1 big division = 10 units.
On the y-axis, 1 big division = 1 unit.
We plot the points A(–4.5,0), B(5.5, 8), C(15.5, 3), D(25.5, 6), E(35.5, 12), F(45.5, 2), G(55.5, 7) and H(65.5, 0).
We draw line segments AB, BC, CD, DE, EF, FG, GH to obtain the required frequency polygon, as shown below.