Ogive

The word Ogive is a term used in architecture to describe curves or curved shapes. Ogives are graphs that are used to estimate how many numbers lie below or above a particular variable or value in data. To construct an Ogive, firstly, the cumulative frequency of the variables is calculated using a frequency table. It is done by adding the frequencies of all the previous variables in the given data set. The result or the last number in the cumulative frequency table is always equal to the total frequencies of the variables. The most commonly used graphs of the frequency distribution are histogram, frequency polygon, frequency curve, Ogives (cumulative frequency curves). In this article, let us discuss one of the graphs called “Ogive” in detail.

Ogive Definition

The Ogive is defined as the frequency distribution graph of a series. The Ogive is a graph of a cumulative distribution, which explains data values on the horizontal plane axis and either the cumulative relative frequencies, the cumulative frequencies or cumulative percent frequencies on the vertical axis. Create the Ogive by plotting the point corresponding to the cumulative frequency of each class interval.

Ogive Graph

The graphs of the frequency distribution are frequency graphs that are used to exhibit the characteristics of discrete and continuous data. Such figures are more appealing to the eye than the tabulated data. It helps us to facilitate the comparative study of two or more frequency distributions. We can relate the shape and pattern of the two frequency distributions. The two methods of Ogives are

  • Less than Ogive
  • Greater than or more than Ogive

Less than Ogive

The frequencies of all preceding classes are added to the frequency of a class. This series is called the less than cumulative series. It is constructed by adding the first-class frequency to the second-class frequency and then to the third class frequency and so on. The downward cumulation results in the less than cumulative series.

Greater than or More than Ogive

The frequencies of the succeeding classes are added to the frequency of a class. This series is called the more than or greater than cumulative series. It is constructed by subtracting the first class second class frequency from the total, third class frequency from that and so on. The upward cumulation result is greater than or more than the cumulative series.

Ogive Chart

An Ogive Chart is a curve of the cumulative frequency distribution or cumulative relative frequency distribution. For drawing such a curve, the frequencies must be expressed as a percentage of the total frequency. Then, such percentages are cumulated and plotted as in the case of an Ogive. Here, the steps for constructing the less than and greater than Ogive are given.

Less than Ogive Construction Steps

  • Draw and mark the horizontal and vertical axes.
  • Take the cumulative frequencies along the y-axis (vertical axis) and the upper-class limits on the x-axis (horizontal axis).
  • Against each upper-class limit, plot the cumulative frequencies.
  • Connect the points with a continuous curve.

Greater than or More than Ogive construction Steps

  • Draw and mark the horizontal and vertical axes.
  • Take the cumulative frequencies along the y-axis (vertical axis) and the upper-class limits on the x-axis (horizontal axis).
  • Against each lower-class limit, plot the cumulative frequencies
  • Connect the points with a continuous curve.

Ogive Example

Question: Construct the more than cumulative frequency table and draw the Ogive for the below-given data.

Marks

1-10

11-20

21-30

31-40

41-50

51-60

61-70

71-80

Frequency

3

8

12

14

10

6

5

2

Solution:

“More than” Cumulative Frequency Table:

Marks

Frequency

More than Cumulative Frequency

More than 1

3

60

More than 11

8

57

More than 21

12

49

More than 31

14

37

More than 41

10

23

More than 51

6

13

More than 61

5

7

More than 71

2

2

Plotting an Ogive:

Plot the points with coordinates such as (70.5, 2), (60.5, 7), (50.5, 13), (40.5, 23), (30.5, 37), (20.5, 49), (10.5, 57), (0.5, 60).

An Ogive is connected to a point on the x-axis, that represents the actual upper limit of the last class, i.e.,( 80.5, 0)

Take x-axis, 1cm = 10 marks

Y-axis = 1 cm – 10 c.f

More than the Ogive Curve:

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