Question

In a school, 100 pupils have heights as tabulate below: 

Height (in cm)	No. of pupils
121 – 130	12
131 – 140	16
141 – 150	30
151 – 160	20
161 – 170	14
171 – 180	8

Find the median height by drawing an ogive.

Answer 1

Exclusive class Intervals	Height (in cm)	No. of pupils	Cumulative Frequency
120.5 – 130.5	121 – 130	12	12
130.5 – 140.5	131 – 140	16	28
140.5 – 150.5	141 – 150	30	58
150.5 – 160.5	151 – 160	20	78
160.5 – 170.5	161 – 170	14	92
170.5 – 180.5	171 – 180	8	100

No. of terms = 100 = N

∴ Median = `100/2` = 50^th term 

Plotting the points (120.5, 0), (130.5, 12), (140.5, 28), (150.5, 58), (160.5, 78), (170.5, 92), (180.5, 100) on graph paper and join them by free hand curve gives the required ogive.

Through mark 50, draw a line parallel to x-axis which meets the curve at A. From A, draw perpendicular to x-axis which meets x-axis at B is the median which is 148 cm.