In a school, 100 pupils have heights as tabulated 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.

The above distribution is discontinuous, converting into continuous distribution, we get :

Adjustment factor = (Lower limit of one class - Upper limit of previous class) / 2

= $\dfrac{131 - 130}{2} = \dfrac{1}{2}$

= 0.5

Subtract the adjustment factor (0.5) from all the lower limits and add the adjustment factor (0.5) to all the upper limits.

Here, n = 100 which is even.

By formula,

Median = $\dfrac{n}{2}\text{ th term} = \dfrac{100}{2}$ = 50th term.

Steps of construction of ogive :

1. Since, the scale on x-axis starts at 120.5, a break (kink) is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 120.5.

2. Take 2 cm along x-axis = 10 units.

3. Take 1 cm along y-axis = 10 units.

4. Plot the point (120.5, 0), as ogive always starts on x-axis representing the lower limit of the first class.

5. Plot the points (130.5, 12), (140.5, 28), (150.5, 58), (160.5, 78), (170.5, 92) and (180.5, 100).

6. Join the points by a free hand curve.

7. Draw a line parallel to x-axis from point A (frequency) = 50, touching the graph at point B. From point B draw a line parallel to y-axis touching x-axis at point C.

From graph, C = 148 cm

Hence, median = 148 cm.