Question

A survey regarding the heights (in cm) of $50$ boys of a class was conducted and the following data was obtained.

Height (in cm)	$140-145$	$145-150$	$150-155$	$155-160$	$160-165$	$165-170$	$170-175$
No. of boys	$12$	$10$	$8$	$9$	$6$	$4$	$1$

Draw both the ogives for the above and hence obtain the median height of the students.

Answer 1

Step 1: Making cumulative frequency table

A more than cumulative frequency distribution can be calculated by adding all the frequencies more than the considered class interval.

And a less than cumulative frequency distribution can be calculated by adding all the frequencies less than the considered class interval.

We prepare the cumulative frequency distribution as follows:

Height (in cm)	No. of boys	Less than cumulative frequency	More than cumulative frequency
$140-145$	$12$	$12$	$50$
$145-150$	$10$	$22$	$38$
$150-155$	$8$	$30$	$28$
$155-160$	$9$	$39$	$20$
$160-165$	$6$	$45$	$11$
$165-170$	$4$	$49$	$5$
$170-175$	$1$	$50$	$1$

Step 2: Drawing the ogive graph to find the median

For less than ogive, we plot the points $\left(145,12\right),\left(150,22\right),\left(155,30\right),\left(160,39\right),\left(165,45\right),\left(170,49\right),\left(175,50\right)$ and

For more than ogive, we plot the points $\left(140,50\right),\left(145,38\right),\left(150,28\right),\left(155,20\right),\left(160,11\right),\left(165,5\right),\left(170,1\right)$

Hence,

From the graph, we see that the ogives intersect each other at $O(151.9,25)$,

Since the abscissa of $O$ is $151.9$, the median height of the students is $151.9cm$.