Question

The following table shows the distribution of the height of a group of factory workers.

Height (cm)	$150-155$	$155-160$	$160-165$	$165-170$	$170-175$	$175-180$	$180-185$
No. of workers	$6$	$12$	$18$	$20$	$13$	$8$	$6$

Determine the cumulative frequencies.

Answer 1

Find the Cumulative Frequency:

Let the number of workers be the frequency $\left(f\right)$,

The Cumulative frequency table is calculated as follows:

Height $\left(cm\right)$	No of workers $\left(f\right)$	Cumulative frequency
$150-155$	$6$	$6$
$155-160$	$12$	$6+12=18$
$160-165$	$18$	$18+18=36$
$165-170$	$20$	$36+20=56$
$170-175$	$13$	$56+13=69$
$175-180$	$8$	$69+8=77$
$180-180$	$6$	$77+6=83$

The total frequency will always be equal to the last cumulative frequency = 83

Final Answer:

The Cumulative frequency for the given height distribution of the group of workers $=83$.