32.

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 following:

(i) the median

(ii) lower Quartile

(iii) if above 158 cm is considered as the tall boys of the class. Find the number of
boys in the class who are tall.

The cumulative frequency table of the given distribution table is as follows:

Plot the points  ( 140, 4 ),  ( 145, 12 ),  ( 150, 32 ),  ( 155, 46 ),  ( 160, 53 ),  ( 165, 59 )  and  ( 170, 60 )  on a graph paper and join them to get an ogive.

No. of boys =  N  = 60

$( \mathrm{i} ) \mathrm{Median} = {\left( \frac{\mathrm{N}}{2} \right)}^{\mathrm{th}} \mathrm{term} = {\left( \frac{60}{2} \right)}^{\mathrm{th}}\mathrm{term} = {30}^{\mathrm{th}} \mathrm{term}$

Through mark  30  on the  Y-axis,  draw a horizontal line which meets the curve at point  A.

Through point  A, on the curve draw a vertical line which meets the  X-axis at point  B.

The value of points  B  on the  X-axis is the median, which is  152.

( ii ) Lower quartile ( Q₁ ) = ${\left( \frac{\mathrm{N}}{4} \right)}^{\mathrm{th}} \mathrm{term} = {\left( \frac{60}{4} \right)}^{\mathrm{th}} \mathrm{term} = {15}^{\mathrm{th}} \mathrm{term} = 148$

( iii ) Through mark of  158  on  X-axis,  draw a vertical line which meets the graph at point  C.

Then through point  C,  draw a horizontal line which meets the  Y-axis  at the  mark of 48.

Thus, number of boys in the class who are tall  =  60 - 48 = 12.