A histogram chart is a powerful way to visualize how data is distributed across different ranges or intervals. Unlike a bar chart that compares categories, a histogram groups numerical data into continuous intervals. This makes it ideal for analyzing frequencies and spotting trends in datasets.
In this guide, you’ll learn the histogram definition and see examples of histograms. In addition, you will explore different shapes like right skewed, left skewed, and bimodal histograms.
Table of Contents
- What Is a Histogram Chart?
- How to Graph a Histogram Chart Step-by-Step
- Understanding the Shapes of Histogram Charts
- Example of a Histogram
- Common Mistakes When Graphing a Histogram Chart
- Tips for Graphing Histogram Charts
- Did You Know About Histogram Charts?
- Frequently Asked Questions About Histogram Charts
- Conclusion
What Is a Histogram Chart?
A histogram chart is a type of bar chart that helps visualize the distribution of numerical data by grouping it into intervals, often called bins. Unlike a standard bar chart, which compares individual categories, a histogram focuses on showing the frequency of data points within each range. This makes it especially useful for identifying patterns such as skewness, central tendency, and variability in a dataset. By examining the shape of a histogram, you can quickly assess whether your data is evenly distributed, clustered, or contains outliers.
A histogram chart is a type of graph used to display how often values occur within a dataset. It groups continuous numerical data into intervals (called “bins”), showing the frequency of values within each range. The height of each bar represents how many data points fall inside that bin.
Unlike a bar chart, where the bars are separated, histogram bars touch each other. This highlights that the data is continuous rather than categorical.
For example, suppose you collected the ages of people in a small group:
| Age Range (Years) | Frequency (Number of People) |
|---|---|
| 10–19 | 3 |
| 20–29 | 4 |
| 30–39 | 8 |
| 40–49 | 2 |
In this sample histogram, the tallest bar corresponds to the 30–39 age range. As a result it show that most people fall within that group. This table provides an ideal dataset for demonstrating how a histogram chart displays frequency distributions.
How to Graph a Histogram Chart Step-by-Step
Before diving into the steps, it’s helpful to understand the main components you’ll be working with: the data, the range of values, and the bins that will organize these values. A histogram graph visually condenses large datasets into a clear representation, making it easier to analyze trends and patterns. Following a systematic approach ensures that the chart accurately reflects the data and provides meaningful insights.
Follow these steps to create a histogram chart manually or in software like Excel or Google Sheets:
- Collect data – Gather a list of numerical values.
- Decide on bins – Divide the data range into equal intervals (e.g., 0–10, 11–20).
- Count frequencies – Tally how many data points fall into each bin.
- Draw bars – Plot bars touching each other to represent each bin’s frequency.
- Label axes – The x-axis shows the intervals, while the y-axis shows frequency.
Once you’ve drawn your histogram graph, you can analyze its shape to understand your data’s distribution.
Understanding the Shapes of Histogram Charts
Histograms can take on different shapes depending on how the data is distributed. By studying the shape of a histogram chart, you can quickly understand key patterns such as symmetry, skewness, or the presence of multiple peaks. Recognizing these shapes, like normal, right skewed, left skewed, and bimodal histograms, helps reveal underlying trends and characteristics in your dataset.
Normal Distribution Histogram Chart
A normal distribution histogram is a visual representation of a dataset where the bars approximate a smooth, symmetrical, bell-shaped curve. This shape indicates that the majority of the data points cluster around the center (the mean), with fewer data points occurring further away from the mean.
Here is a histogram generated from a set of randomly sampled data. It follows a standard normal distribution (μ=0,σ=1), which is a common example of this type of curve:
The histogram visually demonstrates the characteristics of a normal distribution:
- Symmetry: The curve is symmetrical around the central peak (the mean).
- Central Tendency: The highest frequency of data (the tallest bars) is concentrated in the middle.
- Bell Shape: The data values smoothly decrease in frequency as they move away from the center in both directions, forming the characteristic “bell” curve.
The red line overlaid on the histogram represents the Theoretical Probability Density Function (PDF), showing the ideal bell shape that the sampled data’s histogram is trying to approximate. This distribution is fundamental in statistics and is often seen in natural phenomena like human height, weight, and standardized test scores.
Right Skewed Histogram Chart
A right skewed histogram, also known as positively skewed, is characterized by a long tail extending to the right side of the main concentration of data.
This shape means that the mean is typically greater than the median because the extreme high values in the long right tail pull the average in that direction.
Here is the histogram generated from a set of randomly sampled data following a Chi-Squared distribution, which is commonly used to model right-skewed data:
The histogram clearly illustrates the features of a right-skewed distribution:
- Peak on the Left: The majority of the data values are clustered on the lower end (to the left).
- Long Right Tail: There is a gradual decrease in frequency that extends far out to the right. This tail is formed by a small number of extreme high values (outliers).
- Real-World Example: This pattern often appears in distributions like income, where most people earn a moderate salary (the peak on the left), but a small group of very high earners (the long right tail) stretches the graph.
The red line shows the Theoretical Probability Density Function (PDF), representing the ideal right-skewed curve.
Left Skewed Histogram Chart
A left skewed histogram, also known as negatively skewed, is identified by a long tail stretching out to the left side of the data’s peak.
This distribution shape signifies that the majority of data points are concentrated at the higher end of the range, with a small number of low outliers pulling the tail to the left. In this case, the mean is typically less than the median due to those low extreme values.
Here is the histogram generated from a set of randomly sampled data following a Beta distribution (a distribution often used to model left-skewed data):
The histogram clearly illustrates the features of a left-skewed distribution:
- Peak on the Right: The highest frequency of data (the peak) is concentrated on the high-value side (to the right).
- Long Left Tail: A small number of low-value data points stretches the graph far out to the left, creating the long tail.
- Real-World Example: This pattern can be seen in the age of retirement among senior professionals, where most professionals retire at a relatively high, expected age (the peak), but a few might retire much earlier due to unforeseen circumstances (the long left tail).
The red line shows the Theoretical Probability Density Function (PDF), representing the ideal left-skewed curve.
Bimodal Histogram Chart
A bimodal histogram is characterized by the presence of two distinct peaks. This shape typically suggests that there are two different underlying groups or populations within the dataset, each with its own central tendency. Also see the bimodal graph article.
Here is a histogram generated by combining data from two separate normal distributions, illustrating a classic bimodal pattern:
The histogram clearly demonstrates the features of a bimodal distribution:
- Two Peaks: There are two prominent peaks, indicating two points where data values are most concentrated.
- Valley in Between: A dip or valley exists between the two peaks, separating the two clusters of data.
- Overlapping Groups: The distribution often arises when two different datasets are combined, and their respective means are sufficiently far apart to create separate humps, but their distributions might still overlap.
- Real-World Example: This kind of distribution might be seen in test results from two different classes, where each class performed differently, or in height measurements of a group containing both adult men and women, as they typically have different average heights.
Relative Frequency Histogram
A relative frequency histogram displays the proportion or percentage of data points that fall into each bin, rather than the raw counts. This is particularly useful for comparing distributions of datasets with different total numbers of observations, as it normalizes the vertical axis.
Here is the relative frequency histogram:
This histogram illustrates a relative frequency distribution:
- Y-axis as Proportion: The vertical (y) axis now represents the proportion of the total observations that fall into each bin, scaled by the bin width (often referred to as probability density when the area sums to 1). If we wanted exact percentages, the y-axis labels would be 100 times these values.
- Distribution Shape: The shape of the histogram remains the same as a regular frequency histogram for the same data, but the interpretation of the y-axis changes.
- Comparability: Relative frequency histograms are excellent for comparing the shapes and spread of different datasets, even if they have vastly different total sizes. For example, comparing the distribution of test scores from a class of 30 students to a class of 300 students.
The plot shows that the height of each bar corresponds to the relative frequency (proportion per bin width) of data values within that bin.
Example of a Histogram
To see how a histogram works in practice, imagine a teacher analyzing the test scores of a class of students. Instead of listing each score individually, the teacher can group the scores into intervals such as 0–10, 11–20, 21–30, and so on. By plotting these intervals on the horizontal axis and the number of students in each interval on the vertical axis, the teacher creates a histogram that reveals how most students performed and whether there were any exceptionally high or low scores.
To truly understand how histograms work, let’s dive into a concrete example using a small set of data. We’ve gathered the results from 20 student tests, where scores range from 0 to 100. By grouping these raw scores into the score ranges (bins) shown in the table below and counting the frequency of scores within each bin, we can construct a powerful visual representation.
Example of a histogram built from 20 test scores (out of 100):
| Score Range | Frequency |
|---|---|
| 0–20 | 1 |
| 21–40 | 3 |
| 41–60 | 7 |
| 61–80 | 6 |
| 81–100 | 3 |
When plotted, this histogram graph shows a roughly normal distribution histogram, where most students scored in the middle range.
Common Mistakes When Graphing a Histogram Chart
Even small errors in creating a histogram can lead to misleading interpretations of your data. It’s important to understand how the chart’s structure and formatting affect accuracy and readability. By avoiding these common mistakes, you’ll ensure that your histogram correctly represents the data distribution and remains easy to interpret.
- Using unequal bin widths – This distorts the frequency interpretation.
- Leaving gaps between bars – Histograms represent continuous data, so bars should touch.
- Labeling categories incorrectly – Ensure each bin covers a distinct, non-overlapping interval.
- Confusing histograms with bar charts – Bar charts compare categories; histograms show distributions.
Tips for Graphing Histogram Charts
Creating a clear and meaningful histogram takes more than just plotting numbers—it requires thoughtful choices in bin size, labeling, and formatting. These tips will help you make professional-looking histograms that effectively communicate patterns in your data and make comparisons easier across datasets.
- Choose a reasonable number of bins (5–15) for clarity.
- Use consistent intervals for accurate visual comparison.
- Label both axes clearly, including units of measurement.
- For clarity, consider converting frequencies to percentages in a relative frequency histogram.
Did You Know About Histogram Charts?
The histogram was first introduced by Karl Pearson in the late 19th century as part of his work in statistics and probability. Since then, the histogram chart has become one of the most widely used visual tools in data analysis, statistics, and science for identifying patterns and distributions.
Histograms are not just used in schools or basic data analysis, they have applications across many fields, including finance, engineering, quality control, and research. For example, in manufacturing, histograms help monitor product dimensions and identify variations that could indicate defects.
In addition, histograms are closely related to probability distributions in statistics. By examining a histogram of sample data, analysts can make informed guesses about the underlying probability distribution, such as whether the data follows a normal, uniform, or skewed pattern.
Finally, modern data analysis tools like Excel, Google Sheets, and specialized statistical software make creating histograms fast and flexible. These tools often allow users to adjust bin sizes, overlay frequency curves, or compare multiple datasets within the same chart, enhancing both accuracy and visualization clarity.
Frequently Asked Questions About Histogram Charts
What is the definition of a histogram?
A histogram is a type of chart that visually represents the frequency distribution of numerical data. It groups data into continuous intervals, called bins, and uses touching bars to show how many values fall within each range. This makes it easy to see patterns such as concentration, spread, and skewness in a dataset.
What is the difference between a histogram and a bar chart?
A histogram shows continuous numerical data with touching bars, while a bar chart compares categorical data with gaps between bars.
When should I use a histogram chart?
Use a histogram chart to visualize how data points are distributed, especially for continuous variables like time, age, or temperature.
What does a right skewed histogram mean?
A right skewed histogram indicates that most data points are small, with a few large outliers extending the tail to the right.
What does a left skewed histogram show?
A left skewed histogram suggests most values are high, but a few low values pull the tail to the left.
What is a bimodal histogram used for?
A bimodal histogram is used to display data with two distinct peaks, indicating two main subgroups in the dataset.
How is a relative frequency histogram different?
A relative frequency histogram shows percentages or proportions instead of raw counts, allowing for easier comparison between datasets.
Conclusion
A histogram chart is one of the most useful visual tools for understanding data distributions. Whether you’re analyzing test results, financial data, or scientific measurements, histograms reveal how values spread across intervals. Recognizing shapes such as right skewed histograms, bimodal histograms, or normal distribution histograms helps you interpret trends accurately and make informed decisions.