Question

Draw a histogram to represent the following information:

Class interval	5− 10	10 − 15	15 − 25	25 − 45	45 − 75
Frequency	6	12	10	8	18

Answer 1

Here the class intervals are of unequal size. So, we calculate the adjusted frequency using the formula,
$\mathrm{Adjusted}\mathrm{freq}=\frac{\min \mathrm{class}\mathrm{size}}{\mathrm{class}\mathrm{size}\mathrm{of}\mathrm{this}\mathrm{class}}\times \mathrm{freq}$
Class sizes are
10 $-$ 5 = 5
15 $-$ 10 = 5
25 $-$ 15 = 10
45 $-$ 25 = 20
75 $-$ 45 = 30
Minimum class size = 5

Class interval	Frequency	Width of class	Height of rectangle
5-10	6	5	$\frac{5}{5}\times 6=6$
10-15	12	5	$\frac{5}{5}\times 12=12$
15-25	10	10	$\frac{5}{10}\times 10=5$
25-45	8	20	$\frac{5}{20}\times 8=2$
45-75	18	30	$\frac{5}{30}\times 18=3$

​