Question

The following table shows the number of illiterate persons in the age group (10-58 years) in a town:
$\begin{array}{cccccccc}\text{Age group (in years)}& 10-16& 17-23& 24-30& 31-37& 38-44& 45-51& 52-58\\ \text{Number of}& 175& 325& 100& 150& 250& 400& 525\\ \text{illiterate persons}& & & & & & & \end{array}$
Draw a histogram to represent the above data.

Answer 1

Sol:

Given frequency distribution is as below:

Age group (in years)	10-16	17-23	24-30	31-37	38-44	45-51	52-58
No. of illiterate persons	175	325	100	150	250	400	525

The histogram is the graphical representation of a frequency distribution in the form of rectangles, such that there is no gap between any two successive rectangles.

Clearly, the given frequency distribution is in inclusive form, that is there is a gap between the upper limit of a class and the lower limit of the next class.

Therefore, we need to convert the frequency distribution in exclusive form, as shown below:

Age group ( in years)	9.5-16.5	16.5-23.5	23.5-30.5	30.5-37.5	37.5-44.4	44.5-51.5	51.5-58.5
No. of illiterate persons	175	325	100	150	250	400	525

To draw the required histogram, take class intervals, that is the age group, along x-axis and frequencies, that is the number of illiterate persons along the y-axis and draw rectangles. So, we get the required histogram.

Since the scale on x-axis starts at 9.5, a kink (break) is indicated near the origin to show that the graph is drawn to scale beginning at 9.5.