Question

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

Daily income(in Rs)	$100 - 120$	$120 - 140$	$140 - 160$	$160 - 180$	$180 - 200$
Number of workers	$12$	$14$	$8$	$6$	$10$

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

Answer 1

Hint: To represent the data in the table graphically, we mark the upper limits of the class intervals on the x-axis and their corresponding cumulative frequencies on the y-axis by choosing a convenient scale.

Complete step-by-step answer:
The frequency distribution table of less than type is as follows:

Daily income(in Rs)(Upper class limits)	Cumulative frequency
Less than $120$	$12$
Less than $140$	$12 + 14 = 26$
Less than $160$	$26 + 8 = 34$
Less than $180$	$34 + 6 = 40$
Less than $200$	$40 + 10 = 50$

Now, taking upper class limits of class intervals on x-axis and their respective cumulative frequencies on y-axis and then plot the points $\left( {120,12} \right)$,$\left( {140,26} \right)$,$\left( {160,34} \right)$,$\left( {180,40} \right)$&$\left( {200,50} \right)$.

Note: In less than type cumulative frequency curve or an ogive, the points are plotted in the ordered pairs given by (Upper limit, Corresponding cumulative frequency).