Question

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

Ht (cm)	$150-155$	$155-160$	$160-165$	$165-170$	$170-175$	$175-180$	$180-185$
No. of workers	$6$	$12$	$18$	$20$	$13$	$8$	$n=83$$6$

From your graph, write down the median height in cm.

Answer 1

Step 1: Find the Cumulative Frequencies

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

Step 2: Plot the points in the graph and find the median height in cm using the graph:

To plot the $(155,6),(160,18),(165,36),(170,56),(175,69),(180,77)$ and $(185,83)$on the graph

Here $n=83$ , which is odd.

Thus, the median will be,

Median $=\left(\frac{n+1}{2}\right)$th observation

$$\begin{gathered} \frac{n+1}{2}=\frac{83+1}{2} \\ =\frac{84}{2} \\ =42\text{th observation} \end{gathered}$$

Mark the point $42$on the y-axis and mark it as A. From point A, draw a horizontal line that meets the graph at B, then draw a vertical line that meets the x-axis at C.

Point C denotes the median.

Thus, the median is $166.375cm$

Final answer:

From the graph, the median height in cm is $166.375cm$