Histogram - Definition, Types, Graph, and Examples

A histogram is a type of graphical representation used in statistics to show the distribution of numerical data. It looks somewhat like a bar chart, but unlike bar graphs, which are used for categorical data, histograms are designed for continuous data, grouping it into logical ranges, which are also known as "bins."

A histogram helps in visualizing the distribution of data across a continuous interval or period which makes the data more understandable and also highlights the trends and patterns.

Representation of Data in Histogram

In a histogram, data is grouped into continuous number ranges, and each range corresponds to a vertical bar.

• Horizontal axis displays the number range.
• Vertical axis (frequency) represents the amount of data present in each range.

It allows us to assess where the values are concentrated, what the extremes are, and whether there are any gaps or anomalous values. A Histogram is similar to a vertical bar graph, however, the distinction is that a Histogram has no space between the bars, but a bar graph does.

A histogram is a graph that shows the distribution of data. It resembles a sequence of interconnected bars. Each bar represents a range of values, and its height indicates how many data points are inside that range.

Parts of a Histogram

A histogram is a graph that represents the distribution of data. Here are the essential components, presented in simple terms:

• Title: This is similar to the name of the histogram. It explains what the histogram is about and what data it displays.

• X-axis: X-axis is a horizontal line at the bottom of the histogram. It displays the categories or groups that the data is sorted into. For example, if you're measuring people's heights, the X-axis may indicate several height ranges such as "5-6 feet" or "6-7 feet".

• Y-axis: The Y-axis is a vertical line on the side of the histogram. It displays the number of times something occurs in each category or group shown on the X-axis. So, if you're measuring heights, the Y-axis may display how many individuals are in each height range.

• Bars: Bars are the vertical rectangles you see on the chart. Each bar on the X-axis represents a category or group, and its height indicates how many times something occurs inside that category, and the width indicates the range covered by each category on the X-axis. So, higher bars indicate more occurrences, whereas shorter bars indicate fewer occurrences.

Types of Histogram

There are various variations of the histograms based on their shapes:

Uniform Histogram

A Uniform Histogram shows uniform distribution means that the data is uniformly distributed among the classes, with each having a same number of elements. It may display many peaks, suggesting varying degrees of incidence.

Bimodal Histogram

A histogram is called bimodal if it has two distinct peaks. This implies that the data consists of observations from two distinct groups or categories, with notable variations between them.

Symmetric Histogram

Symmetric Histogram is also known as a bell-shaped histogram, it has perfect symmetry when divided vertically down the centre, with both sides matching each other in size and shape. The balance reflects a steady distribution pattern.

Right-Skewed Histogram

A right-skewed histogram shows bars leaning towards the right side. This signifies that the majority of the data points are on the left side, with a few outliers reaching to the right. Consider a histogram showing the distribution of family earnings. A right-skewed histogram occurs when the majority of families are in lower income groups, but a small number of highly rich households skew the average income.

Left-Skewed Histogram

A left-skewed histogram shows bars that lean towards the left side. This means that the majority of the data points are on the right side, with a few exceptionally low values extending to the left. Consider a histogram reflecting the distribution of test scores in a classroom. A left-skewed histogram occurs when the majority of students receive excellent grades but a few do badly, resulting in an average that is dragged to the left.

Frequency Histogram

A frequency histogram visually displays, frequency distribution of how often specific values appear in data. Each bar represents a range of values, with its height indicating the frequency of occurrences. For instance, if we're tracking study hours, the histogram shows how many students fall into each study time range, offering insights into study habits across the student population.

Example: Let’s say we have the ages of 12 people:
Ages: [12, 15, 17, 18, 18, 19, 21, 22, 24, 25, 25, 26]

Frequency Table

Relative Frequency Histogram

Relative Frequency Histogram displays proportions instead of exact counts for each interval. For example, in a class of 20 students, it might show that 25% scored between 70 and 80%. Relative frequency histograms offer insights into the occurrence of distinct values and distribution patterns within a dataset.

Example: Given the test scores of 10 students:

Scores: 55, 60, 62, 70, 75, 78, 80, 82, 85, 90

The frequency table for the scores is as follows:

Relative Frequency Table

Cumulative Frequency Histogram

A cumulative frequency histogram is a graph that depicts the total number of values up to a specific point. Instead of displaying the frequency of each number, it shows the cumulative frequency, which increases as you walk down the graph.

Cumulative Frequency Table

The cumulative frequency table below shows the distribution of test scores for 10 students:

Cumulative Relative Frequency Histogram

A Cumulative Relative Frequency Histogram is a histogram that depicts the percentage of data points in a dataset that fall below a specific number. Each bar indicates the sum of relative frequencies up to a certain point.

Example: Suppose you have exam scores from 10 students:
Scores: 55, 60, 62, 70, 75, 78, 80, 82, 85, 90

Steps to Draw a Histogram

Histogram is the basic tool of representing data, and we can easily draw a histogram by following the steps added below:

Step 1: Collect the data you wish to display in the histogram. This might range from test results to population distribution.

• For example: Assume you get the following test scores: 14, 20, 12, 26, 8, 7, 2, 28, 30, 16, 18, 23.
• First arrange it in ascending order.
  Exam results: 2, 7, 8, 12, 14, 16, 18, 19, 23, 26, 28 and 30.

Step 2: Determine the number of intervals, or "bins," you wish to split your data into. This is determined by the scope and distribution of your data, as well as the amount of information you choose to display. Assume we wish to divide the scores into 5 bins.

Step 3: Determine the limits of each bin. These bounds should encompass the complete range of your data and be regularly spaced.
[0-5 - 10 - 15 - 20 - 25 - 30].

Step 4: Count the number of data points that belong in each bin.

Class Interval	Frequency
0-5	1
5-10	2
10-15	2
15-20	3
20-25	1
25-30	3

Step 5: On a graph, show the bin borders on the x-axis and the frequency of data points in each bin on the y-axis.
Create bars for each bin, with the height of each bar representing the frequency of data points in that bin.

In this histogram, the x-axis depicts the bins, while the y-axis indicates the frequency of data points falling within each bin. The bars represent the sample data's distribution across the given bins.

How to Interpret a Histogram?

A histogram is a type of bar graph that displays the distribution of data. Assume you have a collection of numbers, such as test results or people's heights. A histogram divides these numbers into ranges known as "bins," and then illustrates how many data points fall into each bin by creating bars. The higher the bar, the more data points are contained inside that range.

So, when you look at a histogram, you can immediately observe where the majority of the data is, whether it is grouped in one location or spread out, and whether there are any strange patterns, such as gaps or outliers.

When to Use a Histogram?

Histogram graphs are utilized under various scenarios, and some of them are,

• When you have numbers as data.
• To understand how your data is distributed, especially whether it follows a typical pattern.
• To determine if a process satisfies consumer needs.
• Analyze the results of a supplier's procedure.
• Compare changes in a process over time.
• To compare the results of several processes.
• When you want to quickly and clearly show people how your data is distributed.

Advantages of Histogram

Histograms have various advantages for data analysis and visualization:

• Histograms provide an easy-to-understand visual representation, allowing for a fast estimate of key statistical measures such as the mean and median based solely on the shape and central tendency of the graph.
• Histograms can give insights into probable future data events by highlighting patterns and trends in the current dataset, which can help with forecasting and decision-making.
• Statisticians respect histograms for their consistency since they organize data into intervals with uniform distribution, guaranteeing precision and dependability when showing data distributions.

Histogram Vs Bar Graph

A histogram is one of the most frequent graphs used to represent frequency distribution. The histogram appears more like a bar graph, but there is a distinction between the two. The differences between the bar graph and the histogram are as follows:

Articles Related to Histogram:

• Interpretations of Histogram
• Bar graphs and Histograms

Check other graphical methods to represent data in statistics:

• Bar Graph
• Pie Chart
• Line Graph
• Pictograph
• Frequency Distribution

Histogram Solved Examples

Example 1: Present the following information as a histogram:

Solution:

We take the Marks on the graph's horizontal axis and, based on the first column of the data, set the scale to 1 unit = 10. We pick number of students on the vertical axis of the graph and use the second column of the table to determine the scale: 1 unit = 10. Now we'll create the relevant histogram.

Example 2: Present the following information as a histogram:

Solution:

We take the Marks on the graph's horizontal axis and, based on the first column of the data, set the scale to 1 unit = 10. We pick number of students on the vertical axis of the graph and use the second column of the table to determine the scale: 1 unit = 5. Now we'll create the relevant histogram.