Histogram and Frequency Polygon

What is Histogram?

A histogram is the graphical organization of group data sorted in a user-specified range. It may appear similar to a bar graph; however, the histogram tends to summarise data series so that one can easily interpret them visually and graphically. A histogram also groups multiple data points in logical bins and ranges. 

Additionally, a bar graph-like representation of grouped data accompanies the histogram, wherein the X-axis represents the outcomes. The Y-axis of a histogram indicates the percentage of the number count of occurrences that require evaluation for each data in every column. One can also use the Y-axis for increasing the efficiency of visualized data distributions.

One of the key features of Histogram is that users can customize it as per their requirements. This aspect is beneficial when conducting an in-depth evaluation of data groups. Users can also make changes at X-axis and Y-axis; however, the nature of changes tends to differ.  

For example, the user plots age groups for calculating population in a histogram. Then they can specify the ages in the ranges of 5 years, 10 years, or 20 years as per requirement for analysis. On the other hand, the Y-axis represents the frequency of occurrences in observed data; thus, the changes can be the percentage of total population or evaluation of the total density of population.

Histograms and bar charts tend to be visual representations of grouped data using columns. Therefore, one can often use them interchangeably. However, a histogram is a comparatively more technical tool, as it represents the frequency distribution of variables in a data set. In contrast, bar graphs tend to represent a graphical comparison between discrete variables merely.

Histogram Graph

A histogram graph represents data in the form of a graph and is the simplest visualization of data distributions. 

It divides a set of results ​into columns along the X-axis. The Y-axis represents the multiple occurrences in the data for each column in one histogram. 

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.
• Analyzing a process for determining whether or not it can fulfill 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.

Meaning of Different shapes of Histogram

Following are the different shapes of histogram along with their meaning:

• Normal Distribution: 

The pattern with a bell-shaped curve is known as a normal distribution. In a normal distribution, points are more likely to occur similarly on both sides of the average. The “normal” in this pattern refers to the typical distribution of data for a specific process.

• Skewed Distribution: 

It is asymmetrical, as it naturally limits the outcome to one side, the right or the left. The distribution’s peak is not present in the middle of the graph, and the tail is comparatively far from the head in this sort of pattern. The distribution is called right-skewed or left-skewed in alignment, depending on the direction of the tail.

• Double-Peaked or Bimodal Distribution: 

This pattern looks like the back portion of a camel that has two humps as it has two peaks that are not present in the center of the graph. The outcomes depicted in this pattern represent data of two processes with different distributions combined in a singular set of data.

• Plateau Distribution or Multimodal Distribution: 

This pattern has multiple peaks. Generally, when one combines data of several processes with normal distributions for evaluation through a single graph, the result is a multimodal pattern.

• Edge Peak Distribution: 

This pattern is similar to a normal distribution, but it has a prominent peak in the graph at its head or tail. This pattern generally reflects that the histogram has faulty construction. The key reason for the fault can be the lumping of large data together with the “greater than” symbol.

• Comb Distribution: 

The bars are alternatively short and tall in this distribution. This pattern generally originates from data that is rounded off or from an incorrectly constructed histogram.

• Truncated Distribution: 

This pattern looks like normal distribution; however, it has a very small to no tail.

• Dog Food Distribution: 

This pattern reflects that distributed data is missing something, as there is almost no average in this graph. Most of the time, the distributed data from which truncated data is removed results in dog food distribution.

Frequency Polygon

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 utilized 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.

Conclusion

A histogram is a quick approach to learning about the sample distribution without doing any statistical charting or analysis. The user can easily group data using a frequency polygon. It is a means of displaying statistical data and its frequency visually. 

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.