Graphical Representation
Students construct histograms on the bases of data given in various forms (class size same)
A pictorial representation always gives a better understanding than a written statement. A graphical representation helps us in understanding of a given data in an easier and detailed manner. In order to understand the median of a grouped data properly, we have to draw an ogive.
Firstly, let us discuss what is an ogive?
“When the data is given as ‘less than’ or ‘more than’ type and a graph is plotted between either of the limits and the cumulative frequency, the smooth curve so obtained is known as ogive or cumulative frequency curve”.
Let us discuss with an example that how an ogive is helpful to find out the median of a grouped data.
Let us consider that 80 students of a class appeared in a Geography test. The marks obtained (out of 100) by them are given in the following frequency distribution table.
Table - 1
Marks obtained (out of 100) |
Number of students |
0 − 10 |
2 |
10 − 20 |
1 |
20 − 30 |
3 |
30 − 40 |
5 |
40 − 50 |
9 |
50 − 60 |
15 |
60 − 70 |
22 |
70 − 80 |
12 |
80 − 90 |
7 |
90 − 100 |
4 |
We can write the above table in following two ways.
- Less than type
- More than type
1. For less than type
We can write the given table in less than type as follows.
Marks obtained (out of 100) |
Number of students (Cumulative frequency) |
Less than 10 |
2 |
Less than 20 |
3 |
Less than 30 |
6 |
Less than 40 |
11 |
Less than 50 |
20 |
Less than 60 |
35 |
Less than 70 |
57 |
Less than 80 |
69 |
Less than 90 |
76 |
Less than 100 |
80 |
Construction of Ogive of less than type
The smooth curve drawn between the upper limits of class intervals and cumulative frequency is called cumulative frequency curve or ogive (of less than type). The upper limits of the intervals and cumulative frequency are shown in the above table.
The method of drawing an ogive of less than type is as follows.
(1) Firstly we draw two perpendicular lines, one is horizontal (x-axis) and the other is vertical (y-axis), on a graph.
(2) Now, we mark the upper limits on the horizontal line and the cumulative
frequencies on the vertical line by taking suitable scale.
(3) After this, we plot the points (10, 2), (20, 3), (30, 6), (40, 11), (50, 20), (60, 35), (70, 57), (80, 69), (90, 76), (100, 80). These are the points corresponding to the upp…
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