Draw an ogive for the following frequency distribution :

Class - interval	Frequency
10 - 19	21
20 - 29	15
30 - 39	12
40 - 49	19
50 - 59	8

The above frequency distribution is discontinuous, to convert it into continuous frequency distribution,

$\Rightarrow \text{Adjustment factor} = \dfrac{\text{Lower limit of one class - Upper limit of previous class}}{2} \\[1em] = \dfrac{20 - 19}{2} \\[1em] = \dfrac{1}{2} \\[1em] = 0.5$

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

Continuous frequency distribution for the given data is :

Steps of construction :

1. Since, the scale on x-axis starts at 9.5, a break (kink) is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 9.5.

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

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

4. Ogive always starts from a point on x-axis representing the lower limit of the first class. Mark point (9.5, 0).

5. Take upper class limits along x-axis and corresponding cumulative frequencies along y-axis, mark the points (19.5, 21), (29.5, 36), (39.5, 48), (49.5, 67), (59.5, 75).

6. Join the points marked by a free hand curve.

The required ogive is shown in the below figure: