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 above distribution. Use the graph to estimate the Lower Quartile.

Answer 1

The lower Quartile position is found by:

$Q_1=\frac{60+1}{4}=15.25$

That is to be interpreted as, if the class is put in a line in order of increasing heights from left to right, then the lower quartile range corresponds to the height range of the first $15$ boys (that is the 1st quarter).

So, we find the point on the y-axis that corresponds to $15.25$.

That would be the point $3.05$ on the y-axis.

Next, we find the point on the x-axis which corresponds to the point on y-axis which was found above.

This is shown on the graph.

The required point on the x-axis is $29.125$.

Thus. the lower quartile range is $27-29.125$.

This corresponds to heights $135-146.625cm$.