Histogram: Definition, Example, Properties and Graphs

A chart that shows frequencies for intervals of values of a metric variable is known as a Histogram. This is a form of representation like a bar graph, but it is used for uninterrupted class intervals. Also, it shows the underlying frequency distribution of a set of continuous data.

This allows the examination of the data for its underlying distribution, irregularity, distortion, etc. The group of data is called classes and in the condition of a histogram, they are known as bins because we can think of them as containers that accumulate data and fill up at a rate equal to the frequency of that data class.

Histogram Definition

A histogram is a graphical representation that arranges a group of data into user-specified ranges. Similar to a bar graph, the histogram converts a data series into an easily interpreted visual by taking many data points and grouping them into logical ranges or bins.

Types of Histogram

The classification of histograms can be made based on the frequency distribution of the data. There are four different types of the histogram, they are:

1. Uniform histogram
2. Symmetric or Bell-shaped histogram
3. Bimodal histogram
4. Probability histogram

Uniform Histogram

A uniform-shaped histogram indicates very compatible data. The frequency of each class is very related to that of the others. A data set with a uniform-shaped histogram may be multimodal – having multiple intervals with the maximum frequency. One manifestation of a uniform distribution is that the data may not be split into separate intervals or classes. Another prospect is that the scale of the histogram may need to be adjusted to offer meaningful observations.

Example:

Symmetric or Bell-shaped Histogram

A histogram with a leading ‘mound’ in the centre and related tapering to the left and right. One manifestation of this shape is that the data is unimodal – meaning that the data has a single mode, recognized by the ‘peak’ of the curve. If the shape is symmetrical, then the mean, median, and mode are all unique values. Note that a normally allocated data set creates a symmetric histogram that looks like a bell, leading to the common term for a normal distribution, a bell curve.

Example:

Undefined or Bimodal Histogram

This shape is not particularly defined, but we can note nevertheless that it is bi-modal, having two separated classes or intervals equally representing the maximum frequency of the distribution.

Example:

Probability Histogram

A probability histogram is a graph that constitutes the probability of each outcome on the \(y\)-axis and the possible outcomes on the \(x\)-axis. It is a graphical portrayal of the probability distribution. They are the idealized depiction of the results of a probability experiment. It has a wide range of implementation in statistics.

Example:

Histogram Graphs or Histogram Chart

Histograms are commonly used in statistics to demonstrate how many of a certain type of floater occur within a specific range. For example, a census concentrated on the demography of a country may use a histogram to show how many people are between the ages of \(0-5, 6-10, 11-15, 16-20, 21-25\), etc.

Histograms can be specially made in several ways by the analyst. The first is to change the interval between bins.

The other thought is how to define the \(y\)-axis. The most basic label is to use the frequency of circumstances observed in the data, but one could also use a percentage of total or density instead.

Difference Between Histogram and Bar Graph

Here we have provided the difference between Histogram and Bar Graph:

1. The histogram is a type of bar chart used to constitute statistical information by way of bars to display the frequency distribution of uninterrupted data. It indicates the number of inspections that lie in-between the range of values, which is known as class or bin.
2. A bar graph is used to compare the frequency, total count, sum, or average of data in different classifications by using horizontal or vertical bars. The bar chart is also known as a column chart.
3. A histogram chart helps you to exhibit the distribution of numerical data by providing vertical bars. You can compare non-distinct values with the help of a histogram chart.
4. With the help of a bar graph, you can also do various types of group comparison, which is graphically visualized using a bar chart. Generally, the bar graph will have an axis, label, scales, and bars, constituting measurable values like percentages or numbers.
5. For example, the count of students who got Math subject marks on an exam in various ranges can be visualized using a histogram chart.
6. Bar graphs are used to exhibit all types of data, from quarterly sales, seasonal rainfall to job growth. Once in a while, we can use a double bar graph to evaluate two data sets. It is also used to estimate two or three data sets easily.
7. The histogram refers to a graphical characterization that shows data through bars to display the frequency of numerical data. In contrast, the bar graph is a graphic characterization of data that uses bars to compare different categories of data.
8. The histogram is used to distribute non-distinct variables, while the bar graph is used to compare distinct variables.
9. In the histogram, we cannot regroup the blocks, while in bar charts, it is common to regroup the blocks from highest to lowest. The histogram is used to exhibit the frequency of occurrences, and bar graphs help you compare different categories of data.

Solved Examples on Histograms

Q.1. A teacher wanted to analyze the performance of two sections of students in a mathematics test of \(100\) marks. Looking at their performances, she found that a few students got under \(20\) marks and a few got \(70\) marks or above. So she decided to group them into intervals of varying sizes as follows: \(0-20, 20-30, ….. 60-70, 70-100\). Then she formed the following table:

Ans: We need to make certain changes in the lengths of the rectangles so that the areas are again proportional to the frequencies.

The steps to be followed are given below:

1. Select the class interval with the minimum class size.
2. The lengths of the rectangles are then modified to be proportionate to the class size.

When the class size is \(20\), the length of the rectangle is \(7\). So, when the class size is \(10\), the length of the rectangle will be \(\frac{7}{{20}} \times 10 = 3.5\)

Therefore, the modified table will be as follows.

Since we have calculated these lengths for an interval of \(10\) marks in each case, we may call these lengths as “proportion of students per \(10\) marks interval”. 

So, the correct histogram with varying width is given in the below figure.

Q.2. Given below is a histogram.

How many employees are getting the highest salary?
Ans: From the given data,

The class interval \(25000-30000\) describes the highest salary in rupees.

The bar graph is drawn between \(25000-30000\) gives the number of employees with the highest salary.

The height of a bar graph drawn between the salary range of \(25000-30000\) is \(4\). Hence, there are \(4\) employees who are getting the highest salary.

Q.3. The following table gives the lifetimes of \(400\) LED lamps. Draw the histogram for the below data.

Ans: The histogram for the given data is shown below:

Q.4. The marks obtained by \(40\) students in an examination are given below.

\(27, 18, 15, 21, 48, 25, 49, 29, 27, 21,\)

\(19, 45, 14, 34, 37, 34, 23, 45, 24, 42,\)

\(8, 47, 22, 31, 17, 13, 38, 26, 3, 34,\)

\(29, 11, 22, 7, 15, 24, 38, 31, 21, 35\)

Draw a histogram representing data.

Ans: The given data can be tabulated as

The histogram showing the given data is below:

Q.5. Given below is a histogram.

How many employees are getting the lowest salary?

Ans: From the given data,

The class interval \(0-5000\) describes the highest salary in rupees.

The bar graph drawn between \(0-5000\) gives the number of employees with the lowest salary.

The lowest of a bar graph drawn between the salary range of  \(0-5000\) is \(12\). Hence,\(12\) employees are getting the highest salary.

Summary

In this article, we learned about the definition of histogram charts, types of histograms, and their meaning. We also saw the difference between bar graph and histogram and solved examples on a histogram.

FAQs

Q.1. What is a histogram?
Ans: A chart that shows frequencies for intervals of values of a metric variable is known as a histogram.

Q.2: What is a histogram used for?
Ans: A histogram is a graph that is used to show frequency distributions.

Q.3. What is a histogram? Discuss with example.
Ans: A histogram is a graphical representation that arranges a group of data into user-specified ranges. Similar to a bar graph, the histogram liquifies a data series into an easily interpreted visual by taking many data points and grouping them into logical ranges or bins.

Q.4. What is a histogram vs bar graph?
Ans: 

1. The histogram refers to a graphical characterization that shows data by way of bars to display the frequency of numerical data, whereas the bar graph is a graphical characterization of data that uses bars to compare different categories of data.
2. The histogram distributes non-distinct variables, while the bar graph is used to compare distinct variables.
3. In the histogram, we cannot regroup the blocks, while in bar graphs, it is common to regroup the blocks from highest to lowest. The histogram is used to exhibit the frequency of occurrences, and bar graphs help you compare different categories of data.

Q.5. How do you describe a histogram graph?
Ans: We describe a histogram graph based on the shape. There are three shapes of a histogram graph.

1. Uniform histogram
2. Symmetric or bell-shaped histogram
3. Bimodal or undefined histogram

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