Graphical Representation of Cumulative Frequency Distribution

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 students0 – 1010 – 2020 – 3030 – 4040 – 5050 – 60
No. of students710142063

Solution

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

MarksNo. of studentsLess than cumulative frequencyMore than cumulative frequency
0 – 107Less than 107More than 060
10 – 2010Less than 2017More than 1053
20 – 3014Less than 3031More than 2043
30 – 4020Less than 4051More than 3029
40 – 506Less than 5057More than 409
50 – 603Less than 6060More than 503
    More than 600
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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