# Frequency Polygons

## Frequency Polygons: A Valuable Statistical Tool

A frequency polygon is a graphical representation of a data set with frequency information. It is frequently used to analyze and display grouped statistical data. This type of visual aid is beneficial for trend analysis and recalling data for reference. Here is an example of a frequency polygon:

Example of a frequency polygon, Nilabhro Datta - [website name]

The horizontal axis represents the data point values, while the vertical axis shows the corresponding frequencies. For instance, in the above graph, we can observe that for x = 10, the frequency is 8. Let's explore the steps required to create a frequency polygon and also discuss some crucial considerations for accuracy.

## The Process of Drawing a Frequency Polygon

To draw a frequency polygon based on a grouped frequency distribution, follow these steps:

- Identify the class mark for each class interval and add it as a new column in the distribution table.
- Plot the class marks on the horizontal axis and the frequencies on the vertical axis.
- For each class mark, plot the corresponding frequency on the graph.
- Connect all the plotted points sequentially to form the polygon.

The resulting figure is your frequency polygon. Let's use the following distribution as an example:

Class Class Mark Frequencies5-7 65-9 189-11 2811-13 2713-15 1415-17 2217-35 5

First, we need to calculate the class mark for each class. This can be shown in the following table:

Class Class Mark Frequencies5-7 6 175-9 7 189-11 10 2811-13 12 2713-15 14 1415-17 16 2217-35 26 5

Next, we can plot the points on the graph, with the class marks on the horizontal axis and the frequencies on the vertical axis.

The graph after plotting the requisite points, Nilabhro Datta - [website name]

Finally, we need to connect the plotted points sequentially to get our final frequency polygon.

The final frequency polygon, Nilabhro Datta - [website name]

Some important things to remember when creating a frequency polygon include:

- Use the class mark instead of the class limits to plot the graph.
- If a closed polygon is desired, extrapolate the classes to include the expected next class in either direction and consider the frequency for those classes as 0.

## Frequency Polygons from Histograms

Frequency polygons and histograms are both commonly used to visually represent frequency distributions. While a frequency polygon can be drawn with or without a corresponding histogram, it is easy to obtain a frequency polygon from a given histogram.

To draw a frequency polygon from a histogram, connect the midpoints of the top of each bar in sequential order. This is essentially the same process as before. The midpoint of the top of the bar in a histogram is the class mark, and the top of the bar represents the corresponding frequency. By connecting these points, we can create a frequency polygon. Here is an example:

Frequency polygon from a histogram. Image: ECDC CC BY 4.0

The frequency polygon is obtained by connecting the midpoints of the top of each bar in the histogram.

## Key Takeaways

Frequency polygons are a valuable tool for representing and analyzing grouped statistical data. When creating a frequency polygon, remember to use the class mark instead of the class limits and consider including classes with an expected frequency of 0 for a closed polygon. Additionally, frequency polygons can be easily obtained from histograms by connecting the midpoints of the top of each bar. Keep these tips in mind for accurate and effective use of frequency polygons in statistical analysis.

## Understanding Frequency Polygons: Why They are Essential in Statistical Analysis

Have you ever heard of a frequency polygon? It is a graphical representation of data that is used in statistical analysis. This visual tool is created by connecting the midpoints of the top of each bar in a histogram with straight lines. The resulting figure is your completed frequency polygon.

But what does this mean and why is it important? Well, a frequency polygon serves a crucial purpose in trend analysis and data recall. It provides a more comprehensive and easily interpretable representation of data compared to just looking at numerical values. So, if you are working with a set of grouped data, creating a frequency polygon can greatly enhance your understanding of the data.