Histogram Maker

How to Use the Histogram Maker

This histogram maker turns raw numerical data into a histogram and automatically counts how many observations fall within each bin. To create a histogram using this tool:

1. Enter or paste your numerical values into the Data field.
2. Choose how you want the histogram bins to be created. You can choose automatic, or manually specify the number of bins or bin width for your histogram.
3. Select the number of decimal places you want to display.
4. Click Create Histogram.

After creating the histogram, you can display the bars as frequency, relative frequency, or percentage. You can also show the values above the bars, change the chart title and axis labels, and download the completed histogram as a PNG.

The histogram maker also displays a histogram bins table below the graph to help you see the class interval, frequency, relative frequency, and percentage for every bin.

What Is a Histogram?

A histogram is a graph that shows the distribution of numerical data by grouping observations into intervals called bins or classes. Each bin covers a range of numerical values. The height of the bar shows how many observations, or what proportion of observations, fall within that range.

For example, suppose a histogram of test scores contains the intervals: 50–60, 60–70, 70–80, 80–90. If 12 scores fall between 70 and 80, the bar for that interval represents those 12 observations.

Unlike a regular bar chart, the bars in a histogram touch because the bins represent adjacent parts of a numerical scale.

A histogram helps you see where values are concentrated, how widely they are spread, and the general shape of the distribution.

How to Make a Histogram by Hand

A histogram is built from a frequency distribution. Before drawing the bars, you first divide the numerical scale into intervals and count how many observations fall into each one.

Here’s the step-by-step guide on how to make a histogram manually:

1. Find the minimum and maximum values.
2. Calculate the range.
3. Choose a suitable number of bins or bin width.
4. Create equal-width, non-overlapping intervals that cover the data.
5. Count how many observations fall into each interval.
6. Draw the intervals along the horizontal axis.
7. Draw touching bars whose heights represent the frequencies.

Example: Creating a Histogram

The following values represent the commute times, in minutes, of 24 students:

12, 14, 15, 17, 18, 19, 21, 22, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 39, 41, 43

Create a histogram using a bin width of 5 minutes.

Solution

Step 1: Find the minimum and maximum values

• The smallest observation is: Minimum = 12
• The largest observation is: Maximum = 43

Step 2: Find the range

The range tells us how far the data extend from the minimum to the maximum. The formula is: Range = Maximum − Minimum

Range = 43 − 12

= 31

You can also verify this using the range calculator.

Step 3: Choose the bin width

The question tells us to use a bin width of 5 minutes. Thus, Bin width = 5 minutes

We need intervals of width 5 that cover every observation.

Using a convenient starting point of 10, because it is the smallest whole number below the minimum, we get the following intervals:

• 10 ≤ x < 15
• 15 ≤ x < 20
• 20 ≤ x < 25
• 25 ≤ x < 30
• 30 ≤ x < 35
• 35 ≤ x < 40
• 40 ≤ x ≤ 45

Notice that the intervals do not overlap. A value such as 20 belongs to the 20–25 interval rather than the 15–20 interval.

Step 4: Count the observations in each bin

For 10 ≤ x < 15, the observations are: 12, 14. Therefore: f = 2

For 15 ≤ x < 20: the observations are: 15, 17, 18, 19. Hence, f = 4

If we continue counting the observations in each bin, we can construct the frequency table below.

Check the frequencies: 2 + 4 + 5 + 4 + 4 + 3 + 2 = 24. The total equals the number of observations, so every value has been counted once.

Step 5: Draw the histogram

Place the bin intervals along the horizontal axis and frequency along the vertical axis.

Draw one bar for each interval using the frequencies: 2, 4, 5, 4, 4, 3, 2

The bars should touch because the intervals represent adjoining sections of the same numerical scale.

The tallest bar corresponds to the 20 ≤ x < 25 interval, which contains five commute times.

What Are Bins in a Histogram?

A bin is an interval used to group numerical observations. For example, 0 ≤ x < 10 is one bin, while 10 ≤ x < 20 is another bin. Every observation should fall into exactly one bin.

The number and width of the bins matter because they affect how the histogram looks. Very wide bins combine many observations and may hide important features of the distribution. However, very narrow bins can produce a graph with many irregular bars that makes the overall pattern difficult to see.

For this reason, a histogram should use enough bins to reveal the distribution without making the graph unnecessarily noisy.

Number of Bins vs Bin Width

You can control a histogram using either the number of bins or the bin width. The number of bins tells you how many intervals the data should be divided into. For example, if your data range is divided into five bins, the histogram will contain five adjacent bars.

On the other hand, bin width tells you how wide each interval should be. For example: 20–30, 30–40, and 40–50 have a bin width of 10. A smaller bin width usually creates more bins, while a larger bin width creates fewer bins.

How Does the Automatic Bin Option Work?

If you select Automatic, the histogram maker chooses a sensible starting point for the bins based on the size and range of your dataset.

The tool starts with Sturges’ rule to estimate a suitable number of bins: k = 1 + log₂(n)

where:

• (k) is the estimated number of bins
• (n) is the number of observations

The calculator then uses the range of your data to create readable, equal-width intervals that cover all observations.

Automatic binning is useful when your question does not specify a number of bins or bin width. However, there is no single bin choice that is perfect for every dataset. If the shape looks overly smooth or unnecessarily irregular, try a nearby number of bins or a different bin width and compare the result.

How to Read a Histogram

Don’t focus only on the tallest bar. Read the overall shape of the histogram from left to right.

Therefore, when reading a histogram, the following features are worth noting.

• Center. The center tells you approximately where most of the observations are located. If most of the bars cluster around 60–70, values near that region form the center of the distribution. Remember, a histogram gives you a visual estimate of the center rather than an exact mean or median.
• Spread. Spread describes how widely the observations extend across the horizontal axis. A narrow histogram shows values concentrated within a relatively small range, while a wider histogram indicates greater variability.
• Peaks. A peak occurs where the bars reach relatively high frequencies. A distribution with one clear peak is often described as unimodal. However, if two separate peaks appear, the distribution may be bimodal.
• Skewness. A histogram can also reveal whether a distribution has a longer tail on one side. A right-skewed distribution has a longer tail extending toward larger values. However, a left-skewed distribution has a longer tail extending toward smaller values. A roughly symmetric histogram has a similar shape on both sides of its center.
• Gaps and Possible Outliers. An empty bin creates a visible gap in the histogram. A value or small group of values separated far from most observations may indicate a possible outlier. However, you should examine the original data before deciding that a value is truly an outlier.

Histogram vs Bar Chart

A histogram and a bar chart both use rectangular bars, but they represent different types of data. The table below provides a quick summary of the key differences.

The easiest way to tell the two graphs apart is to look at the horizontal axis. A histogram has numerical intervals, while a bar chart normally has category labels.

Frequently Asked Questions