Question

The following distribution gives the daily income of 50 workers in a factory.

Daily income (in Rs.)	No. of workers
100-120	12
120-140	14
140-160	8
160-180	6
180-200	10

Convert the distribution above to a less than type cumulative frequency distribution and draw its ogive.

Answer 1

Hint: We start solving the problem by recalling the definition of less than type cumulative frequency as the frequency of all the values less than the upper limit of the given class interval. We then add the frequencies which were less than the upper limit of the given class interval. We then make the calculations required to find the cumulative frequencies and draw the plot between the upper limit of class intervals of Daily income and cumulative frequencies.

Complete step-by-step solution:
According to the problem, we are given the daily income of 50 workers in a factory in the following distribution.

Daily income (in Rs.)	No. of workers
100-120	12
120-140	14
140-160	8
160-180	6
180-200	10

We need to convert this distribution to a less than type cumulative frequency distribution and draw its ogive.
We know that the less than type cumulative distribution is calculated by considering all the values less than the upper limit of the given class interval.
So, let us first write the cumulative frequency for the no. of workers.

Daily income (in Rs.)	Less than type cumulative frequency
Less than 120	12
Less than 140	12+14=26
Less than 160	12+14+8=34
Less than 180	12+14+8+6=40
Less than 200	12+14+8+6+10=50

Daily income (in Rs.)	Less than type cumulative frequency
Less than 120	12
Less than 140	26
Less than 160	34
Less than 180	40
Less than 200	50

Now, let us draw the plot between the Upper limit of the class interval of Daily income and less than type cumulative frequency (which is also called ogive).
So, the ogive is as shown below:

Note: We should know that ogive of less than cumulative frequency type is drawn between the upper boundary of class interval and cumulative frequencies. While the ogive of greater than cumulative frequency type is drawn between the lower boundary of class interval and cumulative frequencies. We know that these ogives play an important role while calculating the median of the given frequency distribution. Similarly, we can expect problems to draw the ogive for greater than type cumulative frequencies.