Ogive Curves

Introduction

Since ancient times, the term ogive has been used to describe round or arc shapes. In statistics, ogive curve details when placed on graphs help to calculate the numbers that are below or above a specific variable or value in a set of information. It helps them to know the accurate measurements and the required statistical details. The data availed through this curve is put in a table known as the frequency table.

A frequency table is used to compute the cumulative frequency for developing an ogive graph. This is done by summing the numbers of all the prior specified variables in a data set. In the cumulative frequency table, the overall frequencies of the variables are always equal to the result of the last number. The frequency polygon, histogram, frequency curves, and ogives or cumulative frequency curves are the most widely used graphs for this frequency distribution.

Meaning of Ogive

The frequency distribution graph of a series is known as ogive. The ogive is a cumulative distribution graph in which the horizontal axis represents data values, and the vertical axis represents cumulative relative frequencies, cumulative frequencies, or cumulative percent frequencies. All of the above frequencies up to the current point are referred to as cumulative frequencies. The ogive curve helps us in precisely determining the importance of the available data.

By graphing the point corresponding to the cumulative frequency of each class interval, we may make the ogive. Statisticians widely use the ogive curves to visualize data. It assists in calculating the number of observations that are less than or equal to a specific value.

Ogive Graph

The frequency distribution graphs are frequency graphs that display the features of discrete and continuous data. Figures like these are more visually appealing than tabular data. It aids in the analysis of two or more frequency distributions in comparison. The structure and pattern of the two frequency distributions can be compared.

The two methods that are used in Ogive are :

•       Less than ogive
•       More than ogive

Less than Ogive

The frequencies of all preceding classes are added to the frequency of a class in this form of ogive. This is referred to as a non-cumulative sequence. It is created by multiplying the first-class frequency by the second-class frequency, then by the third. The less-than-cumulative series is the consequence of the downward cumulation.

More than Ogive

The frequency of a class is increased by adding the frequencies of the subsequent classes. More than the cumulative series is the name given to this series. It’s made by deducting the first class frequency from the total, then subtracting the second class frequency from that, and so on. The upward calculation yields a cumulative series greater than or equal to.

Ogive graph

The cumulative frequency distribution curve is what an ogive chart is. When drawing an ogive curve, the frequencies should be stated as a percentage of the overall frequency. The percentages are then added together and plotted, much like an Ogive.

The steps to drawing the less than and greater than ogive are outlined below:

To draw less than ogive:

•       Identify the horizontal and vertical axes by drawing and marking them
•       Take the upper-class limits on the X-axis and the cumulative frequencies on the Y-axis
•       Calculate the cumulative frequencies and plot them against each upper-class limit
•       Create a continuous curve to connect the points

To draw more than ogive:

•       Draw and label the horizontal and vertical axes
•       Plot the lower-class boundaries on the X-axis and the cumulative frequencies along the Y-axis
•       Plot the accumulated frequencies against each lower-class boundary
•       Using a continuous curve, connect the points

Ogive Curve’s Applications

So the application of data availed through the graph has to meet in a point otherwise to find stable data the median of a set of data is obtained. We need to find the media, the data from Ogive Graph are used.  Placing the details available through the curve on the plane and finding the median is easy. The median value is determined by the point where both curves intersect on the x-axis. Ogives are used to compute the percentiles of the data set values and find the medians.

•       In statistics, the ogive graph is used to compute the percentile of a data set’s values and find the data set’s median
•       We can find the median value if both the less than and larger than cumulative frequency curves are displayed on the same graph
•       The median value is determined by where both curves overlap, which corresponds to the x-axis
•       Ogives are used to compute the percentiles of the data set values and find the medians                                                                  Ogive helps in finding percentiles. They help estimate centiles in distribution, just as other representations of cumulative distribution functions. For example, we can determine the central point so that 50% of the observations are below it and 50% are above it. To do so, draw a line from the 50% point on the percentage axis to where it intersects with the curve. The junction is then vertically projected onto the horizontal axis. The value we want comes from the last intersection. The frequency polygon and ogive are used to compare two statistical sets with potentially different numbers.

Conclusion

To understand ogive curves, you can go through the entire article. It will help you understand what ogive curves mean, the methods used in ogive, its meaning, and everything you need to know about ogive curves.