Question

Estimate the median, the lower quartile and the upper quartile of the following frequency distribution by drawing an ogive: 

Age( in yrs)	Under 10	Under 20	Under 30	Under 40	Under 50	Under 60
No. of males	6	10	25	32	43	50

Answer 1

Given data is cumulative data , so draw the ogive as it is .

Age (in yrs) Under	No. of males (f)
10	6
20	10
30	25
40	32
50	43
60	50

Take a graph paper and draw both the axes.

On the x-axis , take a scale of 1cm = 10 to represent the Age (in yrs) under.

On the y-axis , take a scale of 1cm = 10 to represent the no. of males.

Now , plot the points (10,6) , (20,10) , (30,25) ,(40,32) , (50,43) ,(60,5).

Join them by a smooth curve to get the ogive.

No. of terms = 50 

∴ Median = `(25+26)/2` = 25.5^th term

Through mark of 25.5 on y-axis draw a line parallel to x-axis which meets the curve at A. From A, draw a perpendicular to x-axis which meets it at B.

The value of B is the median which is 30.

Lower Quartile (Q₁) = `n/4 = 50/4` = 12.5^th term

Through mark of 12.5 on y-axis draw a line parallel to x-axis which meets the curve at P. From a perpendicular to x-axis which meets it at Q.

The value of Q is the lower quartile which is 22.

Upper Quartile (Q₃) = `(n xx 3)/4 = (50 xx 3)/4` = 37.5^th term

Through mark of 37.5 on y-axis draw a line parallel to x-axis which meets the curve at R. From R, draw a perpendicular to x-axis which meets it at S.

The value of S is the upper quartile which is 44.