Age in years | Less than 10 | Less than 20 | Less than 30 | Less than 40 | Less than 50 |
Number of people | $0$ | $17$ | $42$ | $67$ | $100$ |
(vi)
Marks obtained | More than 10 | More than 20 | Less than 30 | Less than 40 | Less than 50 |
Number of students | $8$ | $25$ | $38$ | $50$ | $67$ |
(v)
Steps to draw a histograms for given frequency distributions,
1. On the x – axis $1cm=10$ units and take the frequency.
2. On the y – axis, take $1cm=10$ units and plot class interval.
Then,
Marks less than | Cumulative Frequency |
$10$ | $0$ |
$20$ | $17$ |
$30$ | $42$ |
$40$ | $67$ |
$50$ | $100$ |
3. So,mark the points in the graph with coordinates having abscissae as actual limits and ordinates as the cumulative frequencies, $(10,0)$, $(20,17)$, $(30,42)$, $(40,67)$, $(50,100)$.
4. Finally join the points plotted by a smooth curve.
(vi)
Steps to draw a histogram for given frequency distributions,
1. Subtract the frequency of each class with the lower bound of the class interval and from the cumulative frequency to get the cumulative frequency distribution.
2. Then mark the following class limits along the x-axis, taking $1cm=10$ units.
3. Also mark the mark cumulative frequency along the y-axis, taking $1cm=10$ units.
Then,
Marks more than | Frequency | Cumulative Frequency |
$10$ | $8$ | $188$ |
$20$ | $25$ | $180$ |
$30$ | $38$ | $155$ |
$40$ | $50$ | $117$ |
$50$ | $67$ | $67$ |
4. So, mark the points (x, f) in the graph, where x is the lower limit of one class and f is the corresponding cumulative frequency $(10,188)$, $(20,180)$, $(30,155)$, $(40,117)$, $(50,67)$.
5. Finally join the points made by a smooth curve.