The graph makes the data easy to understand. So to make the graph of the cumulative frequency distribution, we need to find the cumulative frequency of the given table. Then we can plot the points on the graph.

The cumulative frequency distribution can be of two types –

1. Less than ogive

To draw the graph of less than ogive we take the lower limits of the class interval and mark the respective less than frequency. Then join the dots by a smooth curve.

2. More than ogive

To draw the graph of more than ogive we take the upper limits of the class interval on the x-axis and mark the respective more than frequency. Then join the dots.

Example

Draw the cumulative frequency distribution curve for the following table.

Marks of students	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
No. of students	7	10	14	20	6	3

Solution

To draw the less than and more than ogive, we need to find the less than cumulative frequency and more than cumulative frequency.

Marks	No. of students	Less than cumulative frequency	More than cumulative frequency
0 – 10	7	Less than 10	7	More than 0	60
10 – 20	10	Less than 20	17	More than 10	53
20 – 30	14	Less than 30	31	More than 20	43
30 – 40	20	Less than 40	51	More than 30	29
40 – 50	6	Less than 50	57	More than 40	9
50 – 60	3	Less than 60	60	More than 50	3
				More than 60	0

The best-suited measure of central tendency in different cases and the Empirical relationship between them

i) The mean takes into account all the observations and lies between the extremes. It enables us to compare distributions.

ii) In problems where individual observations are not important, and we wish to find out a ‘typical’ observation where half the observations are below and half the observations are above, the median is more appropriate. Median disregards the extreme values.

iii) In situations which require establishing the most frequent value or most popular item, the mode is the best choice.

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