Histogram

Statistics is a stream of mathematics that is applied in various fields. When numerals are repeated in statistical data, this repetition is known as Frequency and which can be written in the form of a table, called a frequency distribution. A Frequency distribution can be shown graphically by using different types of graphs and Histogram is one among them. In this article, let us discuss in detail about what is a histogram, how to create the histogram for the given data, different types of the histogram, and the difference between the histogram and bar graph in detail.

Table of Contents:

What is Histogram?

A histogram is a graphical representation of a grouped frequency distribution with continuous classes. It is an area diagram and can be defined as a set of rectangles with bases along with the intervals between class boundaries and with areas proportional to frequencies in the corresponding classes. In such representations, all the rectangles 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 other words, histogram a diagram involving rectangles whose area is proportional to the frequency of a variable and width is equal to the class interval.

How to Make Histogram?

You need to follow the below steps to construct a histogram.

  1. Begin by marking the class intervals on the X-axis and frequencies on the Y-axis.
  2. The scales for both the axes have to be the same.
  3. Class intervals need to be exclusive.
  4. Draw rectangles with bases as class intervals and corresponding frequencies as heights.
  5. A rectangle is built on each class interval since the class limits are marked on the horizontal axis, and the frequencies are indicated on the vertical axis.
  6. The height of each rectangle is proportional to the corresponding class frequency if the intervals are equal.
  7. The area of every individual rectangle is proportional to the corresponding class frequency if the intervals are unequal.

Although histograms seem similar to graphs, there is a slight difference between them. The histogram does not involve any gaps between the two successive bars.

When to Use Histogram?

The histogram graph is used under certain conditions. They 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 analyse whether the given process meets the customer requirements.

Difference Between Histogram And Bar Graph

A histogram is one of the most commonly used graphs to show the frequency distribution. As we know that the frequency distribution defines how often each different value occurs in the data set. The histogram looks more similar to the bar graph, but there is a difference between them. The list of difference between the bar graph and the histogram is given below:

Histogram Bar Graph
It is a two-dimensional figure It is a one-dimensional figure
The frequency is shown by the area of each rectangle The height shows the frequency and the width has no significance.
It shows rectangles touching each other It consists of rectangles separated from each other with equal spaces.

The above differences can be observed from the below figures:

Bar Graph (gaps between bars)

Bar graph

Histogram (no gaps between bars)

Histogram

Histogram Types

The histogram can be classified into different types based on the frequency distribution of the data. There are different types of distributions, such as normal distribution, skewed distribution, bimodal distribution, multimodal distribution, comb distribution, edge peak distribution, dog food distributions, heart cut distribution, and so on. The histogram can be used to represent these different types of distributions. The different types of a histogram are uniform histogram, symmetric histogram, bimodal histogram, probability histogram. 

Uniform Histogram

Uniform histogram

A uniform distribution reveals that the number of classes is too small, and each class has the same number of elements. It may involve distribution that has several peaks.

Bimodal Histogram

Bimodal histogram

If a histogram has two peaks, it is said to be bimodal. Bimodality occurs when the data set has observations on two different kinds of individuals or combined groups if the centres of the two separate histograms are far enough to the variability in both the data sets.

Symmetric Histogram

Symmetric histogram

When you draw the vertical line down the centre of the histogram, and the two sides are identical in size and shape, the histogram is said to be symmetric. The diagram is perfectly symmetric if the right half portion of the image is similar to the left half. The histograms that are not symmetric are known as skewed.

Probability Histogram

A Probability Histogram shows a pictorial representation of a discrete probability distribution. It consists of a rectangle centred on every value of x, and the area of each rectangle is proportional to the probability of the corresponding value. The probability histogram diagram is begun by selecting the classes. The probabilities of each outcome are the heights of the bars of the histogram.

Histogram Example

Question: The following table gives the life times of 400 neon lamps. Draw the histogram for the below data.

Lifetime (in hours) Number of lamps
300 – 400 14
400 – 500 56
500 – 600 60
600 – 700 86
700 – 800 74
800 – 900 62
900 – 1000 48

Solution:

The histogram for the given data is:

Histogram example

Frequently Asked Questions on Histogram

Are histogram and bar chart the same?

No, histogram and bar chart are different. In the bar chart, each column represents the group which is defined by a categorical variable, whereas in the histogram each column is defined by the continuous and quantitative variable.

Which histogram represents the consistent data?

The uniform shaped histogram shows consistent data. In uniform histogram, the frequency of each class is similar to one other. In most of the cases, the data values in the uniform shaped histogram may be multimodal.

Can histogram be drawn for the normally distributed data?

Yes, the histogram can be drawn for the normal distribution of the data. A normal distribution should be perfectly symmetrical around its centre. It means that the right should be the mirror image of the left side about its centre and vice versa.

When a histogram is skewed to right?

A histogram is skewed to the right, if most of the data values on the left side of the histogram and a histogram tail is skewed to right. When the data are skewed to the right, the mean value is larger than the median of the data set.

When a histogram is skewed to the left?

A histogram is skewed to the left, if most of the data values fall on the right side of the histogram and a histogram tail is skewed to left. In this case, the mean value is smaller than the median of the data set.

To know more about histograms, graphs and other statistical concepts, visit BYJU’S -The Learning App today!

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