Statistics-Frequency Polygon

Frequency Polygon is a significant statistical concept that requires understanding some basic terms. It is commonly used in economics for presenting data and making it comprehensible.

A frequency polygon is the visual representation tool for demonstrating a data distribution and understanding its shape. The frequency polygon indicates the number of occurrences for every distinct class in a dataset. 

The frequency polygon serves as a curve drawn on the X-axis and Y-axis. The X-axis represents the value in a dataset, while the Y-axis depicts the number of occurrences for categories. 

One can use a histogram and a frequency polygon as alternatives to each other. Both tend to provide perfect shape reflection and visual representation of the data distribution. However, unlike histograms, a frequency polygon can be utilised to compare multiple distributions on a singular graph. 

Use of Frequency Polygon

Following are the uses of the frequency polygon:

• The graph of frequency polygon shows the distribution of cumulative frequency.
• A Frequency polygon sort and represent data and provide the ease of conducting a comparison between data.
• Frequency polygons are easy to understand as they provide a clear and concise view of distributed data.
• Development and assessment of a frequency polygon is less time-consuming than its alternative methods.
• Frequency polygons are among the best tools for comparing similar data types, vast data, and continuous data.

Histogram

Frequency distribution is graphically represented using a histogram, which is a bar graph. The height of a histogram represents the class frequency, and its width represents the class interval. Unlike traditional bar graphs, the bars of a histogram are connected. This is because drawing traditional bar graphs aims to find similarities and differences between different variables. On the contrary, histograms display the distribution of variables on the X and Y axes. 

Histograms with Unequal Class Width 

If you are constructing a histogram with unequal class width, it is important to note that the areas of the rectangles drawn by the histogram must be proportional to the frequencies of every class. 

A histogram is a rectangle. One line of this rectangle is parallel to the baseline, and it is of the same length as the class interval. The vertical line of this rectangle is equal to the magnitude of the frequency density or frequency of the class. 

For classes with unequal widths, you must convert the classes into continuous ones for drawing a histogram. This is because a histogram cannot be drawn for discrete values or ranges. The upper limit of one class compulsorily touches the lower limit of the subsequent class in a histogram. People often skip drawing the common part between 2 rectangles to create a visible impression of continuity.  

Use of Histogram

Histograms are mainly used in statistics to demonstrate the number of occurrences of specific variables within a predetermined range. For instance, a census focusing on the demographic aspects of countries may show the number of individuals of different ages or gender ratios in different states. 

It is advisable to use a histogram in the following conditions:

• Data that needs evaluation is numerical.
• Shaping data distribution to determine whether the output derived from data evaluation is normally distributed in the data groups.
• Analysing a process for determining whether or not it can fulfil the users’ requirements.
• Evaluating output from different perspectives of different users.
• Evaluate whether there is a noticeable change in the process over different periods.
• Determining whether outputs of two or more processes are different from different perspectives.
• Establishing communication between the distributed data quickly and easily.

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

Conclusion :

A frequency polygon resembles a histogram; it compares data sets or depicts a cumulative frequency distribution. A line graph is used to show quantitative data. It makes the facts simple to comprehend. In some cases, one can combine a histogram and a frequency polygon to depict the distribution form better.