Question

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

(i) $\begin{array}{ccccccc}Classinterval& 10-15& 15-20& 20-25& 25-30& 30-35& 35-40\\ Frequency& 10& 15& 17& 12& 10& 8\end{array}$

(ii) $\begin{array}{cccccc}Classinterval& 10-19& 20-29& 30-39& 40-49& 50-59\\ Frequency& 23& 16& 15& 20& 12\end{array}$

Answer 1

(i)

Class Interval	Frequency
10-15	10
15-20	15
20-25	17
25-30	12
30-35	10
35-40	08

Steps of construction:

(a) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.

(b) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

( c) Join the mid-points of the rectangle to obtain the ogive.

(ii)

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:

(a) Convert the data into exclusive form.

(b) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.

(c) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

(d) Join the mid-points of the rectangle to obtain the ogive.