Question

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

Class Interval	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Frequency	4	12	21	18	15	7	3

Answer 1

We first construct the cumulative frequency table of the given distribution.

Class Interval	Frequency (f)	Cumulative Frequency
0-10	4	4
10-20	12	16
20-30	21	37
30-40	18	55
40-50	15	70
50-60	7	77
60-70	3	80

Take a graph paper and draw both the axes .

On the x-axis , take a scale of 1 cm = 10 to represent the class intervals.

On the y-axis , take a scale of 1 cm = 10 to represents the frequency .

Now , plot the points (10,4),(20,16),(30,37),(40,55),(50,70),(60,77),(70,80)

Join them by a smooth curve to get the ogive.

No. of terms = n = 80

∴ Median = `(40+41)/2` = 40.5^th term         

Through mark of 40.5 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 32.

Lower Quartile (Q₁) = `n/4 = 80/4` = 20^th term

Through mark of 20 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 23.

Upper Quartile (Q₃) = `(n xx 3)/4 = (80 xx 3)/4` = 60^th term

Through mark of 60 on y-axis draw a line parallel to x-axis which meets the curve at R. From R, draw a perpendicular to -axis which meets it at S.

The value of S is the upper quartile which is 43.5.