Question

The heights of trees in a forest are given as follows. Draw a histogram to represent the data.

Heights in metre	$16-20$	$21-25$	$26-30$	$31-35$	$36-40$	$41-45$	$46-50$	$51-55$
Number of trees	$10$	$15$	$25$	$30$	$30$	$50$	$35$	$20$

Answer 1

In this problem, the given class intervals are discontinuous(inclusive) form. If we draw a histogram as it is, we will get gaps between the class intervals. But in a histogram the bars should be continuously placed without any gap. Therefore we should make the class intervals continuous. For this we need an adjustment factor.
Adjustment Factor$=\frac{1}{2}\left[\text{(lower limit of a class interval)-(upper limit of the preceding class interval)}\right]$
$=\frac{1}{2}(21-20)=0.5$
In the above class interval, we subtract $0.5$ from each lower limit add $0.5$ in each upper limit. Therefore we rewrite the given table into the following table.

Heights in metre	$15.5-20.5$	$20.5-25.5$	$25.5-30.5$	$30.5-35.5$	$35.5-40.5$	$40.5-45.5$	$45.5-50.5$	$50.5-55.5$
Number of Trees	$10$	$15$	$25$	$30$	$45$	$50$	$35$	$20$

Now the above table becomes continuous frequency distribution. The histogram is given below.