**What Is Histogram?**

A

Histogramis the graphical or visual representation of the distribution of categorical numeric data in a dataset. We can create them using theAnalysis ToolPakor thePivot Table, and by using the formulas. We can create theHistogram Formulausing theFREQUENCYandCOUNTIFSformulas.

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

##### Table of contents

### 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**

**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:

You are free to use this image on your website, templates, etc, Please provide us with an attribution linkHow to Provide Attribution?Article Link to be Hyperlinked

For eg:

Source: Histogram Formula (wallstreetmojo.com)

**Excel VBA – All in One Courses Bundle (35+ Hours of Video Tuto**rials)

**–>>** **If you want to learn Excel and VBA professionally**, then Excel VBA All in One Courses Bundle (35+ hours) is the perfect solution. Whether you’re a beginner or an experienced user, this bundle covers it all – from **Basic Excel to Advanced Excel, Macros, Power Query, and VBA.**

### #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:

**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.****Now, count the number of data points gathered.****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****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 =****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****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.****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.

- 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.
- 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.
- 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.

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

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

**So, the Area of the Histogram will be –**

**Therefore, the Area of the Histogram = 47 children.**

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

### 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.

- The concept of a
**Histogram**equation is very useful as it portrays a set of data. Although a**Histogram**looks quite similar to a bar chartBar ChartBar charts in excel are helpful in the representation of the single data on the horizontal bar, with categories displayed on the Y-axis and values on the X-axis. To create a bar chart, we need at least two independent and dependent variables.read more, the end-use of a**Histogram**is very different from that of a bar chart. - A
**Histogram**is useful in displaying a large amount of data in a more understandable way, which is easy to visualize. - It also captures the frequency density of each class interval. We can determine the median and the distribution of data from a
**Histogram**. Also, the skewnessSkewnessSkewness is the deviation or degree of asymmetry shown by a bell curve or the normal distribution within a given data set. If the curve shifts to the right, it is considered positive skewness, while a curve shifted to the left represents negative skewness.read more of the distribution can be selected as if the bars on the left or the right are higher. Then, it indicates that the data is skewed, or otherwise, the data is symmetrical. - A
**Histogram**primarily finds its application in the case of large-scale exercises like a nationwide census, which may be conducted every ten years. In such cases, the data is compiled and presented in a**Histogram**so that we can easily study it. Also, in the cases of surveys where a**Histogram**is created, anyone who can interpret the**Histogram**can use the data later for further studies or analysis.

### 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 **Histogram**s 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.**Step 2: **Click the “**Options**” tab.

The “**Excel Options**” window opens. Click the “**Add-ins**” option on the left.**Step 4: **In the “**Manage**” drop-down, choose the “**Excel Add-ins**” option, and click “**Go…**”.**Step 5: **This will open the “**Add-ins**” window. Check the “**Analysis ToolPak**” checkbox, and click “**OK**”.

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

### Recommended Articles

This article is a guide to Histogram Formula. Here we learn to use & interpret formula, chart, graphs, types, relevance, examples, downloadable excel template. You may learn more about fixed income from the following articles: –