# What is a Histogram – Definition, Advantages & Examples

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Graphs and charts are effective visual tools because they present information quickly and easily. Because of this reason graphs are commonly used by print and electronic media. There are various ways data can be presented in a graphical form. One such widely used graphical representation of data is the histogram.

A histogram can be defined as a set of rectangles with bases along with the intervals between class boundaries. The heights of rectangles are proportional to corresponding frequencies of similar as well as for different classes.

A histogram looks similar to a bar graph but there is a difference between these two types of graphical representation. Let’s understand what is a histogram and how is it read and drawn using examples.

## What is a Histogram?

A histogram is a graphical representation of a grouped frequency distribution with continuous classes. It is a type of area diagram which is drawn as a set of rectangles with bases along with the intervals between class boundaries. These areas are proportional to frequencies in the corresponding classes.

The rectangles in a histogram are adjacent since the base covers the intervals between class boundaries. The heights of rectangles are proportional to corresponding frequencies of similar classes and for different classes, the heights will be proportional to corresponding frequency densities.

In simpler terms, a histogram is a diagram involving rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.

Similar to a bar graph, a histogram is also drawn over two axes. The $x$-axis of a histogram shows the continuous class intervals being compared, and the $y$-axis represents the scale. A scale is a set of numbers that represents the data. The title of the histogram provides a general overview to the reader of what is being measured and compared.

The histogram can also be a horizontal histogram. In the case of a horizontal histogram, the $x$-axis represents the scale showing the data and the $y$-axis shows the continuous class intervals being compared.

## Characteristics of a Histogram

A histogram possesses certain characteristics which must be studied to get more knowledge about it. These are as follows,

• The width of the bars represents class intervals.
• Frequency is indicated by the height of a bar in a histogram.
• A histogram has no space or gap between two bars. The data is continuous.
• Non-distinct variables are present inside a histogram.
• Bars of a histogram are not flexible and therefore cannot be reordered.

## How to Read a Histogram?

The different steps to make a bar are given below:

Step 1: Check whether the given histogram is a horizontal histogram or a vertical histogram.

Step 2: In the case of a vertical histogram, the class interval are present on the horizontal axis (or $x$-axis) and the frequencies are represented by the vertical bars(or rectangles).

In the case of a horizontal histogram, the class intervals are present on the vertical axis (or $y$-axis) and the frequencies are represented by the horizontal bars(or rectangles).

Step 3: For each class interval,

in the case of a vertical histogram note down the point on the $y$-axis corresponding to the height of a vertical bar

in the case of a horizontal histogram note down the point on the $x$-axis corresponding to the length of a horizontal bar

### Examples

Let’s consider an example to understand how a histogram is read.

Ex 1: Following histogram shows the frequency distribution of marks obtained by students in English test.

• How many students scored marks between 20 and 25?
• How many students scored less than 15?
• How many students scored more than 10?
• How many students appeared in the test?

The height of the bar corresponding to the class interval 20 – 25 is 5. Therefore, the number of students scoring between 20 and 25 is 5.

The number of students scoring less than 15 falls under the class intervals 5 – 10 and 10 – 15.

The number of students scoring between 5 – 10 is 2 and the number of students scoring between 10 – 15 is 10. Therefore, the number of students scoring less than 15 is 12 (2 + 10).

The number of students scoring more than 10 falls under the class intervals 10 – 15, 15 – 20, and 20 – 25.

The number of students scoring between 10 – 15 is 10, between 15 – 20 is 18 and the number of students scoring between 20 – 25 is 5. Therefore, the number of students scoring more than 10 is 33 (10 + 18 + 5).

Number of students who appeared for the test is 35(2 + 10 + 18 + 5).

## How to Draw a Histogram?

The different steps to draw a histogram are given below:

Step 1: Choose a suitable scale to represent weights on the horizontal axis.

Step 2: Choose a suitable scale to represent the frequencies on the vertical axis.

Step 3: Draw the bars(rectangles) corresponding to each of the given weights using their frequencies.

### Examples

Let’s consider an example to understand how a histogram is drawn for the given data.

Ex 1: Draw a histogram for the following frequency distribution table showing the heights of students in a class.

To draw a vertical histogram, we choose the height of students(class intervals) for the $x$-axis and the number of students(frequency) for the $y$-axis.

Since the maximum number of students in a class interval is $15$, so the $y$-axis is scaled to accommodate numbers up to $20$.

Finally, draw the histogram that represents the number of students in class intervals. While drawing a histogram, it should be noted that there should not be any space between two adjacent bars.

Note: The zig-zag line on the horizontal axis in the beginning after zero (0) is called a kink. It is drawn on the x-axis near the origin when the scale on the axis does not start from zero. A kink denotes the missing divisions.

## When To Use Histogram?

The histogram graph is used under certain conditions. These are

• The data should be numerical.
• A histogram is used to check the shape of the data distribution.
• Used to check whether the process changes from one period to another.
• Used to determine whether the output is different when it involves two or more processes.
• Used to analyze whether the given process meets the customer’s requirements.

## Difference Between Histogram and Bar Chart

The major difference between a histogram and a  bar chart is the bars of the bar chart are not just next to each other. In a histogram, the bars are adjacent to each other. Following are the differences between a histogram and a bar chart.

## Practice Problems

Below is the frequency distribution of the height of 50 students in a class. Draw a histogram of the given data.

Draw a histogram of the following data

The number of workshops organized in a school in different areas during the last five years is given. Draw a histogram of the data.

## FAQs

### What is a histogram used for?

The histogram is a popular graphing tool. It is used to summarize discrete or continuous data that are measured on an interval scale. It is often used to illustrate the major features of the distribution of the data in a convenient form.

### What is a histogram vs a bar graph?

Histograms visualize quantitative data or numerical data, whereas bar charts display categorical variables. In most instances, the numerical data in a histogram will be continuous (having infinite values). You should not attempt to display all possible values of a continuous variable along an axis.

### Is a histogram always a bar chart?

Although histograms are made up of bars, they are not bar charts. Histograms show distributions, bar charts compare categorical values.

## Conclusion

A histogram is a graphical representation of a grouped frequency distribution with continuous classes. It is a type of area diagram which is drawn as a set of rectangles with bases along with the intervals between class boundaries. The basic difference between a histogram and a bar chart is histograms visualize quantitative data or numerical data, whereas bar charts display categorical variables.