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.
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|
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|
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.