Histogram
2026-02-21 20:29 Diff
https://brightchamps.com/en-us/math/data/histogram

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Last updated on November 21, 2025

A histogram is a statistical representation of numbers to show how often something occurs in different groups. The objective here is to make patterns easy to spot. Data is grouped into bins (intervals) to display the frequency. This article talks about histograms in detail.

What is a Histogram?

A histogram is a type of bar graph used to show how often things happen within different ranges of values. It is made up of rectangles placed right next to each other, with no gaps between them, because the data is continuous.
 

  • The width of each rectangle shows the class interval (the range of values).
  • The height or area of each rectangle shows the frequency (i.e., how many times the values fall within that range).
     

In short, a histogram uses connected rectangles to show how data is spread across different ranges.

Difference Between Histogram and Bar Graph

A Histogram and a Bar Graph both use bars to represent data, but they are used for different purposes and follow different rules.
 

Bar Graph Histogram Shows different categories (like fruits, colors, subjects). Shows number ranges or continuous data (like 0–10, 10–20). Bars have gaps between them. Bars are joined with no gaps. The order of bars can be changed. The order of bars cannot be changed because ranges follow a sequence. Used for qualitative data. Used for quantitative data. Each bar represents a single category. Each bar represents a range (class interval).

Parts of Histogram


A histogram is a graph that helps you understand how data is distributed. It has four main parts:
 

  • Title - The title tells you what the histogram is showing and what kind of data it represents.
  • X-axis - The X-axis (the horizontal line) displays the groups or ranges of data, for example, if the histogram shows people's heights, the X-axis may have ranges like “4-5 feet” or “7-8 feet”.
  • Y-axis - The Y-axis (the vertical line) shows how many values fall into each group. In the height example, it tells you how many people are in each height group.
  • Bars - The bars are the vertical rectangles in the histogram. Each bar represents a range from the X-axis. The height of the bar shows how many values are in the range; taller bars mean more data, and shorter bars mean less data.

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Types of Histogram

In this section, let’s learn about types of histograms. Based on the type of frequency, histograms can be classified into:

  • Normal Distribution
  • Skewed Distribution
  • Double-Peaked Distribution
  • Plateau Distribution
  • Edge Peak Distribution
  • Comb Distribution
  • Truncated Distribution
  • Dog Food Distribution

Normal Distribution - A normal distribution is the common pattern seen in histograms. The normal distribution is also known as a bell-shaped histogram because of its curve, which has a single peak at a specific time interval.  

Skewed Distribution - The skewed distribution is skewed in one direction, either to the right or left. The skew to the right is a right-skewed distribution, and the one to the left is a left-skewed distribution.


Double-Peaked Distribution - Double-peaked distribution is also known as bimodal; as the name suggests, it has two peaks. It is the outcome of two processes with different distributions in one set of data. 

Plateau Distribution - Plateau distribution is the combination of many processes in one data set.
 

Edge Peak Distribution - Edge peak distribution looks similar to the normal distribution, but has one large peak in the tail.
 

Comb Distribution - Comb distribution has alternative large and small bins; it can be because either the data is rounded off or incorrectly constructed. 
 

Truncated Distribution - Truncated distribution is also known as heart,cut distribution. It is also similar to a normal distribution with no tail.


Dog Food Distribution - Dog food distribution refers to unevenly distributed data where most values cluster in one group, leaving very few in others.

How to Make a Histogram?

To make a Histogram, first group your numerical data into ranges. Then draw bars showing how many values fall into each range to visualize the distribution.


Step 1: First gather your data and group it into equal groups into equal intervals. These intervals help organize the value.


Step 2: Next, make a table. Write down each interval and note how many values fall into it. This count is called the frequency.


Step 3: Draw the axes the x-axis will show the intervals, and the y-axis will show the frequency. Make sure to label both axes clearly so it's easy to understand.


Step 4: Finally draw the bars. Use the information from your table, each bar should rise up to the correct frequency. Taller bars mean more data in that interval, and shorter bars mean less.

When to Use a Histogram?

Use a Histogram when you want to understand how numerical data is distributed across different ranges. It is best for continuous data like scores, ages, temperatures, or measurements.
 

  • When your data contains numbers, and you want to organize it visually.
     
  • To see how the data is spread out and whether it follows a common pattern.
     
  • To check if a process is working well and meeting customer expectations.
     
  • To study and understand how a supplier is performing.
     
  • To track how a process changes over a period of time.
     
  • To compare the performance of different processes.
     
  • When you want to show people the distribution of your data simply and clearly.

How to interpret a Histogram?

Interpreting a histogram is easy if you focus on a few things:
 

  • Look at the height of the bars : Taller bars mean more people or items fall in that range. Shorter bars mean fewer.
  • Notice the overall shape: See if the graph looks balanced, shifted to one side, or has more than one peak. This shows how your data is distributed.
  • Check where most values are grouped : Find the interval with the tallest bar,that’s where most of your data lies.

Advantages and Disadvantages of a Histogram

Here is a simple and easy description of the advantages and disadvantages of a histogram, written clearly for beginners:
 

Advantages of Histogram Disadvantages of Histogram It provides a clear picture of how your data is distributed. You cannot read exact values from a histogram, only ranges. You can easily see which values occur the most or the least. It can be clear if the intervals (class sizes) are not chosen properly. It helps you understand patterns, such as whether data is balanced or skewed. You cannot use it for very small data sets. It’s useful for comparing changes in a process over time. It only works for numerical data, not categories.

Applications of Histogram

Histograms are used in different fields to compare data, spot trends, identify patterns, and so on. So, let’s learn a few applications of histograms. 

  • In business, histograms are used to compare data, analyze sales, product quality, and so on.
  • To identify the outcome of a common process, we use a histogram; it does not take much time to understand the data given in a histogram. 
  • A histogram is used to analyze the disease incidence, treatment outcome, patient's history, etc. 

Tips and Tricks to Master Histogram


Here are some simple tips to remember when creating a histogram:
 

  • Choose an appropriate scale for the y-axis (vertical axis). Pick a number that evenly divides most of your frequencies to make the graph neat and easy to read.
  • Use a histogram only for continuous data. It’s meant to show data that flows smoothly from one value to the next.
  • Histograms help you quickly understand how your data is distributed. They show patterns at a glance.
  • The axes don’t always have to start from 0. You can begin from another number if it makes the graph clearer.
  • Make sure the bars touch each other. There should be no gaps because the data ranges are continuous.
  • Parents can use histograms to quickly see how data is spread.
  • Teachers help students to spot learning trends, strengths, and areas that need support.
  • Children can think of a histogram like sorting things into groups.

Common Mistakes and Ways to Avoid Them in Histogram

Mistakes are common when working with histograms. In this section, we will learn more about some common mistakes and the ways to avoid them. 
 

Real Life Application of a Histogram


Understanding students' performance: Teachers use a histogram to see how many students scored within certain mark ranges in a test. This helps identify who needs support and who is excelling.


Tracking children's growth: Parents and doctors use histograms to compare children's height or weight ranges to determine whether they fall within healthy growth ranges.


Customer Feedback Analysis: Companies use histograms to improve service quality by analyzing how many customers rated their service as poor, average, or good. This helps them improve quality.


Daily Temperature Monitoring: Weather departments create histograms to show how often specific temperature ranges occur in a month. This helps people plan activities and farmers plant crops.


Quality Control in Factories: Histograms are used to check the proper size or weight of products at factories. If any items are too big or too small, it is a sign of a wrong production process.

Download Worksheets

Problem 1

A class of 52 students took a math test, and their scores are recorded as follows:

Okay, lets begin

Explanation

 The Histogram is of the score range in the x-axis and the number of students in the y-axis.
 

Well explained 👍

Problem 2

A store recorded the daily sales (in $100s) for 30 days as follows:

Okay, lets begin

Explanation

The Histogram is plotted with the sales range on the x-axis and the number of days on the y-axis.
 

Well explained 👍

Problem 3

The heights of 45 students (in cm) are given in the following table:

Okay, lets begin

Explanation

Here, The Histogram is plotted with height in cm on the x-axis and the number of students on the y-axis. 

Well explained 👍

Problem 4

The speed of 37 bikes (In KM) are given in the following table:

Okay, lets begin

Explanation

Here, The Histogram is plotted with speed Range on the x-axis and the number of Bikes on the y-axis.

Well explained 👍

Problem 5

The Age (In Office) are given in the following table:

Okay, lets begin

Explanation

 Here, The Histogram is plotted with Age on the x-axis and count on the y-axis.

Well explained 👍

FAQs on Histogram

1.What is a histogram in one line?

A histogram is a visual representation of data to show how frequently different ranges of numbers occur in a dataset. 

2.What are the four parts in a histogram?

The title, x-axis, y-axis, and bars are the four parts of a histogram. 
 

3.How to calculate the frequency for a histogram?

To calculate the frequency, we should count the number of data points that fall within each bin range. 
 

4.How do we calculate the mean for a histogram?

The mean of a histogram is calculated by using the formula:

\(x̄ = {{(f . x_m)} \over f }\)where f is the frequency of each bin; \(x_m\) denotes the midpoint of each bin; \((f . x_m)\) is the sum of products of bin midpoints and frequency; f indicates the total number of data points.

5.What is the range of a histogram?

The difference between the maximum and the minimum values shown in a data set is the range of the histogram.
 

Jaipreet Kour Wazir

About the Author

Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref

Fun Fact

: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!