Question

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

Marks (less than)	10	20	30	40	50	60	70	80
No. of students	5	15	30	54	72	86	94	100

Answer 1

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

Marks (less than)	No. of students (f)
10	5
20	15
30	30
40	54
50	72
60	86
70	94
80	100

Take a graph paper and draw both the axes.

On the x-axis , take a scale of 1 cm = 10 to represent marks less than.

On the y-axis , take a scale of 1 cm = 20 to represents the number of students.

Now , plot the points (10,5), (20,15),(30,30),(40,54),(50,72),(60,86),(70,94),(80,100).

join them by a smooth curve to get the ogive.

No. of terms = 100

`therefore` Median = `(50 + 51)/2` = 50.5^thterm

Through mark of 50.5 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 is at B.

The value of B is the median which is 38.

Lower Quartile (Q₁) = `n/4 = 100/4` = 25^th term

Through mark of 25 on y-axis draw a line parallel to x-axis which meets the curve at P .From P , draw a perpendicular to x-axis which meets it at Q.

The value of Q is the lower Quartile which is 28.

Upper Quartile (Q₃)  = `(n xx 3)/4 = (100 xx 3)/4` = 75^th term

Through mark of 75 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 51.