Histogram Formula

Article byWallstreetmojo Team
Edited bySheeba M
Reviewed byDheeraj Vaidya, CFA, FRM

What Is Histogram?

A Histogram is the graphical or visual representation of the distribution of categorical numeric data in a dataset. We can create them using the Analysis ToolPak or the Pivot Table, and by using the formulas. We can create the Histogram Formula using the FREQUENCY and COUNTIFS formulas.

For example, we can represent the student data, such as scores, height, weight, etc., graphically, as shown below.

histogram formula graph

Key Takeaways

  • The Histogram Formula helps us to understand large datasets in a pictorial way when plotted in a graph.
  • We can plot a Histogram formula’s Histogram graph in 3 different types, namely, Uniform, Symmetrical, and Bimodal Histogram.
  • To plot a graph, we need a minimum of 2 variables for the X and Y Axes. So, we must take the large data, categorize it in different bins or buckets to reduce the size of the data to get it in the form of frequencies or periods, calculate using the formula, and then plot the graph.

Histogram Excel Chart Explained In Video

Histogram Formula

The Histogram Formula is used to visually represent a dense numerical data set. It is derived by segregating the numerical data at regular intervals and plotting them on a graph. The graph consists of the X-axis where the intervals are plotted, the Y-axis shows the values, and the bars show the value of the data in coherence with their intervals.

For example, if we have data related to students’ scores and need to create a distribution of students’ scores. In such a scenario, we can use the Histogram and make a graphical representation of students’ scores that can easily condense the given data set, interpret, visually analyze the data points, and group them into logical ranges or bins, enabling us an organized group of data points into user-specified ranges.

The formula for the Histogram revolves around the Area of the bars. It is simple and is calculated by the summation of the product of the frequency density of each class interval and the corresponding class interval’s width. The Area of the Histogram Formula is mathematically represented as:

Area-of-Histogram-Formula

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Source: Histogram Formula (wallstreetmojo.com)

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#Explanation of the formula of the Histogram

We can derive the formula for the calculation of the Area of the Histogram by using the following seven steps:

  1. Firstly, it is to be decided on how we measure the process and what we should collect as data. Once determined, the data is gathered and presented in a tabular form, such as a spreadsheet.

  2. Now, count the number of data points gathered.

  3. Next, determine the range of the sample, which is the difference between the maximum and minimum values in the data sample.

    Range = Maximum value – Minimum value

  4. Next, determine the number of class intervals that can be based on either of the following two methods,

    As a thumb rule, use 10 as the number of intervals, or
    The number of intervals can be calculated by the square root of the number of data points, which is then rounded to the nearest whole number.


    Number of intervals = Histogram formula eg1

  5. Now, determine the width of the interval class by dividing the range of the data sample by the number of intervals.

    Class width = Range / Number of intervals

  6. Next, develop a table or spreadsheet with frequencies for each interval. Then, derive the frequency density for each interval by dividing the frequency by the corresponding class width.

  7. Finally, the Area for the Histogram equation is calculated by adding the product of all the frequency density and their corresponding class width.

#How To Read the Histogram example and its interpretation?

Now that we understand the basics and different types of this concept, it is vital to understand how to read and interpret the data after it is converted into a Histogram. Let us do so through the step-by-step guide mentioned below.

  1. The first step is to recognize the dependent and independent variables within the set. For instance, if we are collecting data relating to the height of students in ABC school, the independent variable would be the height, and the dependent variable would be the frequency or the number of students.
  2. Once the data is collected, they have to segregate into different groups based on their frequency in different ‘bins’. For example, there might be 4 students with a height of 5’7” and 5 with 6’1”. In simpler words, students of the same height will be grouped for differentiation.
  3. After the collection of data, the different intervals can be plotted against different heights on the graph. Once the data is plotted, one can analyze the data and find similarities and differences or find the mean height of the whole data set.

Examples

Let us understand the concept of Histogram Formula Excel with the help of the following examples.

You can download this Histogram Formula Excel Template here – Histogram Formula Excel Template

Let us consider the table below, which shows children’s weights in a class.

Example 1.1

From the above table, we can calculate the following:

  • Class width of the first interval = 35 – 30 = 5
  • Class width of the second interval = 45 – 35 = 10
  • Class width of the third interval = 50 – 45 = 5
  • Class width of the fourth interval = 55 – 50 = 5
  • Class width of the fifth interval = 65 – 55 = 10

Again,

  • Frequency density of the first interval = 2 / 5 = 0.4
  • Frequency density of the second interval = 7 / 10 = 0.7
  • Frequency density of the third interval = 21 / 5 = 4.2
  • Frequency density of the fourth interval = 15 / 5 = 3.0
  • Frequency density of the fifth interval = 2 / 10 = 0.2

For the Histogram Formula calculation, we will first need to calculate class width and frequency density, as shown above.

Hence, Area of the Histogram = 0.4 * 5 + 0.7 * 10 + 4.2 * 5 + 3.0 * 5 + 0.2 * 10

Example 1.2

So, the Area of the Histogram will be –

Exampe -1.3
  • Therefore, the Area of the Histogram = 47 children.

A graphical representation of the weight of children is shown below:

histogram formula graph

Relevance And Uses Of Histogram

Let us understand the relevance and uses of a frequency density Histogram Formula and other related factors through the discussion below.

Important Things To Note

  • When we display a Histogram formula graphically, we must make sure that there are no gaps between the displayed Bars. We can use the Format Data Series for the same.
  • Ensure to sort the data in an increasing or decreasing order to plot the graph in an evenly way for better understanding.

Frequently Asked Questions

1. What are the different types of Histograms?

The different types of Histograms based on the distribution of different frequencies to better interpret them after the data points have been plotted on the graph are,
Uniform: It indicates that the number of classes within the data set is too small. Moreover, each class represents the same number of elements that might have multiple peaks.
Symmetric: It is also referred to as a bell-shaped Histogram. If a vertical line is drawn from the center of the graph, either side of the graph is identical in size and shape.
Bimodal: If a distribution has two peaks, it is referred to as a bimodal distribution. It is commonly found when the opinions or observations of two types of individuals are analyzed.

2. Give some information on the Formula of the Histogram.

Karl Pearson first introduced this term to visually represent data and analyze the numbers within each interval of the data set. Usually, the X-axis shows the intervals, the Y-axis displays the values, and the bars represent the value of the data.
The Histogram Formula in Excel is said to be more complicated as it takes more time and effort than frequency distribution. It is most useful when the data size is large and needs to be simplified for documentation or analysis. For instance, nationwide data such as census is collected every decade, the data could be overwhelming to asses in its raw form. Therefore, it is converted into a Histogram using the frequency density Histogram Formula for easy understanding and analysis.

3. How to enable Analysis ToolPak to use Histogram?

Analysis ToolPak in Excel will not be found in an Excel workbook by default.
The steps to enable Analysis ToolPak are listed as follows.

Step 1: Select the File tab.

File

Step 2: Click the “Options” tab.

File - Option

The “Excel Options” window opens. Click the “Add-ins” option on the left.

Histogram - Add Ins

Step 4: In the “Manage” drop-down, choose the “Excel Add-ins” option, and click “Go…”.

Histogram - Step 4

Step 5: This will open the “Add-ins” window. Check the “Analysis ToolPak” checkbox, and click “OK”.

Histogram - Step 5

Now, we will see the “Data Analysis” option under the Data tab.

Histogram - Step 5 - Data Analysis.jpg

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