Question

Use Graph paper for this question. A Survey regarding height (in cm ) of $60$ boys belonging to Class $10$ of a school was conducted. The following data was recorded.

Height in cm	$135-140$	$140-145$	$145-150$	$150-155$	$155-160$	$160-165$	$165-170$
No. of boys	$4$	$8$	$20$	$14$	$7$	$6$	$1$

Taking $2$cm $=$ height of $10$cm along one axis and $2$cm $=10$ boys along the other axis draw an ogive of the distribution. Use the graph to estimate the median.

Answer 1

There are $60$ boys.

To find the median height, we first arrange the class into increasing order of heights and then pick the height of the middle student as the median height.

To find that on the ogive plot, we have to find the mark on the y-axis which corresponds to $30$ boys and that would be the point $6$ on the y-axis.

Thus, the point on the x-axis which corresponds to the point $6$ on the y-axis is the median height.

We find that the number $6$ on the y-axis corresponds to somewhere between $29$ and $30$ on the x-axis.

That means, the median height range is $145-150cm$.

This is shown on the graph attached.