| Class Interval | $1–10$ | $11–20$ | $21–30$ | $31–40$ | $41–50$ |
| Frequency | $8$ | $12$ | $10$ | $16$ | $6$ |
Solution:-
Steps to draw histograms for given frequency distributions,
1. First we have to make the class intervals continuous by subtracting 0.5 from the lower limit of each class and add 0.5 to the upper limit of each class.
Then we have,
| Class Interval | $0.5–10.5$ | $10.5–20.5$ | $20.5–30.5$ | $30.5–40.5$ | $40.5–50.5$ |
| Frequency | $8$ | $12$ | $10$ | $16$ | $6$ |
2. On the x – axis, take $1cm=5$ units and plot frequency.
3. On the y – axis, take $1cm=5$ units and plot class interval.
Then,
| Class Interval | Class mark | Frequency |
| $0.5–10.5$ | $(0.5+10.5)/2=11/2=5.5$ | $8$ |
| $10.5–20.5$ | $(10.5+20.5)/2=31/2=15.5$ | $12$ |
| $20.5–30.5$ | $(20.5+30.5)/2=51/2=25.5$ | $10$ |
| hg | $(30.5+40.5)/2=71/2=35.5$ | $16$ |
| $40.5–50.54$ | $(40.5+50.5)/2=91/2=45.5$ | $6$ |
3. So, in the graph mark the points $(5.5,8)$, $(15.5,12)$, $(25.5,10)$, $(35.5,16)$, $(45.5,6)$.
4. Also mark two more midpoints of zero frequency on x – axis at the start and at the end.
5. Finally Connect the points using straight lines.