100 pupils in a school 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

Draw the ogive for the above data and from it determine the median (use graph paper).

Converting the discontinuous data into continuous data.

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

$= \dfrac{131 - 130}{2} \\[1em] = \dfrac{1}{2} \\[1em] = 0.5$

1. We construct the table as under :

2. Take 1 cm along x-axis = 10 cm

3. Take 1 cm along y-axis = 10 (people)

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

5. Plot the points (130.5, 12), (140.5, 28), (150.5, 58), (160.5, 78), (170.5, 92) and (180.5, 100) representing upper class limits and the respective cumulative frequencies.
   Also plot the point representing lower limit of the first class i.e. 120.5 - 130.5.

6. Join these points by a freehand drawing.

The required ogive is shown in figure above.

Here, n (no. of students) = 100.

To find the median :

Let A be the point on y-axis representing frequency = $\dfrac{n}{2} = \dfrac{100}{2}$ = 50.

Through A draw a horizontal line to meet the ogive at P. Through P, draw a vertical line to meet the x-axis at M. The abscissa of the point M represents height = 147.5 cm.

Hence, the median height = 147.5 cm.