Group 2 ReportOgive

Definition

• Ogive is a graph of a cumulative distribution, which shows data values on the horizontal axis and the cumulative frequencies, the cumulative relative frequencies or cumulative percent frequencies on the vertical axis.

• It is one of the most commonly used graphs of frequency distribution.

• Ogive is defined as the frequency distribution graph of a series.

• It is also known as the cumulative frequency curve.

Ogive chart

• An Ogive Chart is a curve of the cumulative frequency distribution or cumulative relative frequency distribution.

• To draw such a curve, first of all the simple frequency must be expressed as percentage of the total frequency. Then, such percentages are cumulated and plotted as in the case of an ogive.

2 ways of constructing an Ogive chart

1.Less than Ogive Chart

2.Greater than Ogive Chart

Less than Ogive chart (Less than cumulative frequency

curve)1. Draw and label the horizontal and vertical axes.

2. Take the cumulative frequencies along the y axis (vertical axis) and the upper class limits on the x axis (horizontal axis)

3. Plot the cumulative frequencies against each upper class limit.

4. Join the points with a smooth curve

Example• Less than Ogive chart

- When we write, 'less than 10 - less than 0', the difference gives the frequency 4 for the class interval (0 - 10) and so on.

Greater than Ogive chart (Greater than cumulative frequency curve)

Less than

1. Draw and label the horizontal and vertical axes.

2. Take the cumulative frequencies along the y axis (vertical axis) and the lower class limits on the x axis (horizontal axis)

3. Plot the cumulative frequencies against each lower class limit.

4. Join the points with a smooth curve.

Example• Greater than Ogive chart

- When we write 'more than 0 - more than 10', the difference gives the frequency 4 for the class interval (0 - 10) and so on.

Note

•Corresponding to the point of intersection of less than cumulative frequency curve, greater than or more than cumulative frequency curve is the Median of the distribution. So, we can find the middlemost value of the series if we draw the less than and greater than Ogives.

Example

• Question: Draw the more than cumulative frequency curve for the following data

Class  10-20  20-30  30-40  40-50  50-60 60-70  70-80 80-90 

F 3 15 8 20 7 4 6 2

Solution

• First lets find the more than cumulative frequency corresponding to each class. For this the frequencies of the succeeding classes are added to the frequency of a class. The greater than cumulative frequency table is given below.

Greater than Ogive chart

Lower limit Frequency More than  Cumulative Frequency 

10  3 65

20 15 65 - 3 = 62

30  8 62 - 15 = 47

40  20 47 - 8 = 41

50  7 41 - 20 = 19

60  4 19 - 7 = 12

70  6 12 - 4 = 8

80  2 8 - 6 = 2

• Now we draw the horizontal and vertical axes and label them. Plot the cumulative frequencies corresponding to the lower limit of each class and join the points using a smooth curve.

Example

Solution

Ogive Graph