# Cumulative frequency polygon

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A number of repeating events in a given time is called frequency. Cumulative frequency is a frequency polygon that shows total frequencies by giving the amount of the multitude of past frequencies up to the current point. The combined percentages are added to the diagram from left to right. A cumulative frequency polygon is also known as an Ogive. Ogive curve assists with discovering a few precise details like the popularity of the given information or the probability of the data that fall inside a specific frequency range. An ogive chart plots the boundaries along the x-axis and the cumulative frequency on the y-axis.

## Difference Between Ogive And Cumulative Frequency Polygon:

Ogive is a frequency polygon that shows cumulative frequencies or gives a plot of total values. In contrast, in the Cumulative frequency polygon, the frequency is added to each subsequent frequency, and the number of perceptions is set apart with only one point at the midpoint of a stretch.

After this, a straight line is developed associating every one of the focuses, which later gives the actual portrayal of the diagram.

Ogive is not the same as a frequency polygon since it is a plot of cumulative data rather than a plot of the data itself.

## Conditions In Which Cumulative Frequency Polygon Is Used:

1. Cumulative frequency polygons address quantitative data when the data stretches don’t approach the number of particular values in the informational index. This is consistently the situation for continuous data. When the information is discrete, it is feasible to address each value in the dataset on the x-pivot.
2. Utilizing a cumulative frequency graph is a decent method for tracking the median average and interquartile range. The interquartile range is a proportion of how fanned out the information is. It is more solid than the reach since it does exclude outrageous qualities like extraordinarily high or low qualities. The quartiles with the middle split the information into four equivalent parts.
3. Ogives are helpful in distributions to assess centiles. It makes it easier to find the central point so that half of the perceptions would be underneath this point and half above. To achieve this, we make a line from the place of the half-percent axis of the percentage until it crosses with the bend. Then after that, we forecast the intersection in an upward direction onto the horizontal axis. The last crossing point gives us the ideal value.
4. The frequency polygon and ogive are utilized to look at two measurable sets whose number could be unique.

## Purpose of a Cumulative Frequency Polygon

A line graph is utilized in cumulative frequency polygons to address or represent quantitative information.

Cumulative frequency polygon assists us with noticing and seeing how the values inside a specific data set change. It helps us observe and find out the number of information perceptions under a particular scope of data sets.

It also permits us to rapidly gauge the number of observations that are not precisely equivalent to a specific value.

Ogives are additionally utilized in registering the percentiles of the informational index values.

### For Example:

70 percent of the time, information focuses are underneath that value, and 30 percent of the time, they are over that value.

## What Does a Cumulative Frequency Polygon Show?

Cumulative frequency polygon portrays the shape and patterns of the data. It is typically drawn with the assistance of a histogram; however, it can be removed without it also.

The cumulative frequency polygon is not just assistance to ensure that the information is figured out and addressed; they are additionally going to make it more straightforward for individuals to look into every one of the outcomes. These are a lot more obvious, and they give a detailed image of the dispersion of information.

## How to Find The Cumulative Frequency?

The cumulative frequency is determined by adding every frequency from a frequency table to the number of its ancestors. The last worth will be equivalent to the absolute for all observations since all frequencies will have been added to the past aggregate.

For example, let’s say we need to find the cumulative frequency of the students and the scores they got in the last test. Firstly, we need to arrange our data (scores) from the smallest to most considerable value in the frequency table.

Scores = x

Frequency (no of students) = f

Cumulative frequency = cf

We will make three columns in the frequency table. The first column contained scores that each student got, the second for the number of students, and the third for calculating the cumulative frequency.

 Scores, x Frequency, f cumulative frequency, cf 3 4 4 4 2 5 6 6 5 7 8 8 5 9 4

The first no in the cumulative frequency column is always the same as the first frequency number. So we will write 4. Then we will add the first cf value to the second f value and write the sum in the cf box.

 Scores, x Frequency, f cumulative frequency, cf 3 4 4 4 2 6 5 6 12 6 5 17 7 8 25 8 5 30 9 4 34 In this way, we will solve and find all the cf values in the table.

## How to Draw a Cumulative Frequency Curve?

Once you’ve completed calculating cumulative frequency, it’s time to start drawing the graph.

All the scores will go on the x-axis, and all the cf values will go on the vertical or y-axis.

Draw a line graph with the x-axis equal to the values of your data set and the y-axis equal to the cumulative frequency. Make class intervals, and then in the middle of each class interval, mark a point at the height corresponding to the frequency. We can create a curve by connecting these locations or points with smooth curves in a sequence. This graphical representation of a cumulative frequency distribution is the cumulative frequency curve.