Basics about the ogive statistics

We consider the following types of graphical representation of frequency distribution in statistics.
(1) Histogram or Area diagram
(2) Frequency polygon
(3) Ogive or cumulative frequency distribution graph
We shall discuss a bit in detail about the ogive graph in this article. The curve that is obtained by plotting cumulative frequencies against their respective class boundaries is called an cumulative line graph. As such there are two types of cumulative line graph – the less than the cumulative line graph and the more than cumulative line graph. The less than cumulative line graph is obtained by using the less than type cumulative frequency on the vertical axis to plot the cumulative line graph. The more than cumulative line graph is obtained by using the more than type of cumulative frequency on the vertical axis to plot the cumulative line graph. The points thus plotted are then joined successively by short line segments. The graph thus obtained is called an ogive graph.

Ogives may be considered useful for obtaining quartiles graphically. The more than type and the less than type cumulative line graph intersect in a point. If a perpendicular line is drawn from the point of intersection of the two cumulative line graph (more than type and less than type) on the horizontal axis, then the x co ordinate of this point gives us the value of the median, also called the second or the middle quartile.
Q gives are very useful in making short term projections.

Example:
The ages of students in the anatomy class are shown in the following frequency table.
Age Interval(yrs) Frequency
15 - 17                    13
18 – 20                    15
21 – 23                    20
24 – 26                    10
27 – 29                     8
30 – 32                     4
Draw an ogive for the above data.
Solution: First lets add a cumulative frequency column to that table:
Age Interval(yrs) Frequency Cumulative frequency
15 - 17                     13                    13
18 – 20                     15                    28
21 – 23                     20                    48
24 – 26                     10                    58
27 – 29                      8                            66
30 – 32                      4                            70

The cumulative line graph can now be plotted using the upper limit of class interval on the x axis and the cumulative frequency on the y axis as follows:

Ogive Graph

The above graph represents the cumulative line graph of the given example problem question.