Question

Draw a cumulative frequency curve (ogive) for the following distributions:

Class Interval	10 – 19	20 – 29	30 – 39	40 – 49	50 – 59
Frequency	23	16	15	20	12

Answer 1

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

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

= `(20 - 19)/2`

= `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.

Class Interval (Inclusive)	Class Interval (Exclusive)	Frequency	Cumulative Frequency
10 – 19	9.5 – 19.5	23	23
20 – 29	19.5 – 29.5	16	39
30 – 39	29.5 – 39.5	15	54
40 – 49	39.5 – 49.5	20	74
50 – 59	49.5 – 59.5	12	86
		Total	86

Steps of construction of ogive:

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 = 10 units along the x-axis.
3. Take 1 cm = 10 units along the y-axis.
4. Ogive always starts from a point on the x-axis, representing the lower limit of the first class. Mark point (9.5, 0).
5. Take upper-class limits along the x-axis and corresponding cumulative frequencies along the y-axis, and mark the points (19.5, 23), (29.5, 39), (39.5, 54), (49.5, 74) and (59.5, 86).
6. Join the points marked by a free-hand curve.

The required ogive is shown in the below figure: