Statistics >> Ogive
An ogive is a graph of cumulative frequencies of a frequency distribution of continuous series. In drawing an ogive the class boundaries are plotted on the x-axis and the cumulative frequencies on the y-axis and the resulting curves are known as gives.
Ogives are of two types
(i) Less Than Ogive: Here' less than' cumulative frequencies are plotted against upper class boundaries of the respective class intervals.
(ii) More Than Ogive : Here 'greater than' cumulative frequencies are plotted against the lower class boundaries.
Less than ogive is an increasing curve and more than ogive is a decreasing curve.
The foot of the perpendicular from the intersection of two ogives gives the value of median.
Uses of-Ogives
Ogives are useful for locating partition values viz. Median, Quartiles, Deciles, Percentiles etc. They are also useful to determine the number of proportion of items above or below a particular value. With the help of ogive we can compare more than one distributions.
Location of partition values from ogives
Various partition values can be located graphically with the help of ogives. First of all, we draw an ogive by plotting the given data on a graph. For finding positional values, we mark the position of frequency on y-axis and draw a line from this mark till it intersects with the ogive. From this point of intersection we draw a vertical line meeting x-axis. The point where the like touches the x-axis is the required positional value.
Example 7: Draw two gives from the following data.
|
Class
|
Frequency
|
|
20-25
25-30
30-35
35-40
40-45
45 50
50-55
55-60
|
6
9
13
23
19
15
9
6
|
From your ogive find median, first quartile, first decile and 60th percentile.
Solution: First we shall calculate cumulative frequency
|
Class
|
Frequency
|
Cumulative Frequency
|
|
|
|
Less than
|
More than
|
|
20-25
25-30
30-35
35-40
40-45
45-50
50-55
55-60
|
6
9
13
23
19
15
9
6
|
6
15
28
51
70
85
94
100
|
100
94
85
72
49
30
15
6
|
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