Question

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

Marks	30-40	40-50	50-60	60-70	70-80	80-90	90-100
No. of boys	10	12	14	12	9	7	6

Answer 1

Marks	No. of boys (f)	Cumulative Frequency
30-40	10	10
40-50	12	22
50-60	14	36
60-70	12	48
70-80	9	57
80-90	7	64
90-100	6	70

Take a graph paper and draw both the axes.

On the x-axis, take a scale of 1cm = 20 to represent the marks.

On the y-axis , take a scale of 1 cm = 10 to represent the number of boys.

Now , plot the points (40,10),(50,22),(60,36),(70,48),(80,57),(90,64),(100,70)

Join them by a smooth curve to get the ogive.

No. of terms = 70

∴ Median = `(35+36)/2` = 35.5^th term

Through mark of 35.5 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 60.

Lower Quartile (Q₁) = `n/4 = 70/4` = 17.5^th term

Through mark of 17.5 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 47.5.

Upper Quartile (Q₃) = `(n xx 3)/4 = (70 xx 3)/4` = 52.5^th term

Through mark of 52.5 on y-axis draw a line parallel to x-axis which meets the curve at R, draw a perpendicular to x-axis which meets it at S.

The value of S is the upper quartile which is 74.5.