Histogram: Types, Graph & Examples

A histogram can be simply defined as the graphical representation of data which is continuous using rectangles. It is a two-dimensional figure whose purpose is to achieve accurate probability distribution.

• Histogram is used to represent numerical data, which is not accurate.
• The first step in the creation of this figure involves data binning, or bucketing or discrete binning.
• It involves reducing the effects of minor observation errors.
• Karl Pearson discovered this theory in 1891 to give an insight about the previous or past data. 
• The process helps in summarizing the continuous data.
• Histograms are easy to work with and are used in many fields like medicine, hydrology, stock exchange, and photography. 

Key Terms: Histogram, Frequency, Rectangular bars, Number, Numerical data, Bar chart, Probability, Probability Distribution, Graph, Two-dimensional figure, Uniform distribution, Symmetric histogram, Bimodal histogram, Probability histogram 

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What is Histogram?

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A histogram is a graphical representation of the distribution of numerical data to the most approximate value. These are in the form of rectangular bars present adjacent to each other. 

• Each bar is unique and denotes a different numerical data and frequency type. 
• Frequency is the number of times a data appears in the distribution. 
• There is a separate table for frequency distribution. 
• These bars or bins may vary in their respective widths.

The x-axis represents the class interval, and the y-axis represents frequencies corresponding to different class intervals. English mathematician Karl Pearson first introduced the idea of a histogram. 

• The main purpose of a histogram is to assess probability distribution. 
• This provides a very clear picture of the values lying in the distribution. 
• They throw light on the nature of data, like where it is concentrated and where it is missing.
• It is used in many digital image processing programs.
• Histograms are often used in contrast to a bar chart. 
• It is important to note that the data in a histogram is continuous, whereas the same is often missing in bar charts. 

Histogram

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Characteristics of Histogram

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

• Width of the bars represent class intervals.
• Frequence is indicated by the height of a bar in a histogram.
• A histogram has no space or gap between two bars. 
• Non-distinct variables are present inside a histogram.
• Bars of a histogram are not flexible therefore cannot be reordered.

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Histogram Graph

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Histogram graph is defined as the graphical representation of data using bar graph. It is the simplest way to represent data distribution.

• The range of outcomes is represented along the columns.
• It is represented along the x-axis.
• The count or multiple occurrences of the data is represented along y-axis.

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How to plot Histogram?

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The steps to plot the histogram are as follows:

• Start the process by first marking the class intervals on the x-axis and frequency on the y-axis.
• The scale of both axes are the same, and class intervals are exclusive.
• Now, draw the rectangle of bases as class intervals corresponding to frequencies as heights.
• The height of this rectangle is proportional to class frequency in case intervals are equal.
• The area of each rectangle is proportional to class frequency.

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Types of Histogram

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Histogram is classified under four important heads depending upon the kind of frequency which is distributed. 

Uniform Histogram

The nature of data present in a uniform histogram is very consistent. It denotes almost the same number of values in each bar. Every bar in a uniform histogram is almost of the same size or height.

Symmetric Histogram 

Symmetric histogram, more popularly known as the bell-shaped histogram, is named after its structure. It is such that there appears to be a centre and all the values surrounding it continuously.

• As we move towards the sides from the centre, the value seems to be decreasing.
• A bell-shaped histogram represents a normal distribution. 
• In this type of histogram, a vertical line is drawn at the centre and the sides as it keeps decreasing in an equal number.
• Therefore, they are symmetrical. 

Bimodal Histogram 

A bimodal histogram has two bars with the same height or two peaks. As there are two centres here, two types of data are denoted. The data, in this case, should be clear and properly analysed.

• These histograms are easily identifiable. 

Right-skewed Histogram 

When a histogram is skewed to the right, it means the values are positive. This distribution of data popularly occurs in large numbers on the left side of a histogram.

• The frequency of their occurrence is very low on the right side.
• A right-skewed distribution takes place when the data inside a histogram has a low range, like 0.
• It denotes that the entire data has values bigger than zero. 

Left-skewed Histogram

In left-skewed histograms, distribution occurs towards the left and is said to be negatively skewed. This is quite contrary to the right skewed histogram. You can easily identify this type of histogram by seeing a tail going towards the left.

• We can figure out that the frequency decreases as we move to smaller numbers.
• Collected data has values less than 100 here, which means the observations are less. 

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Parts of Histogram

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Histogram consists of four essential parts so as to work efficiently. Each of these parts has a specific function to fulfil to contribute to the ultimate goal of a histogram. These are described as follows:

Title 

The title serves as the most crucial part of a histogram. It is because of the title that readers get an idea on what it is about. It consists of the overall gist and information regarding the histogram. 

X-axis

The x-axis of a histogram indicates the scale of values present inside a histogram. It is an interval by nature and relates to values so as to pave way for the measurements falling under it. 

Y-axis 

It is that part of the histogram which represents the number of times a value or values occur within those intervals of x-axis. The y-axis relates to frequency.

Bars

The bar is important because its height determines the frequency of the values occurring within the intervals. In this case the width of the bar indicates the data interval which is already over. 

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Applications of Histogram

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The applications of histogram are as follows:

Normal Distribution

When the curve is in the shape of a bell, then it is called a normal distribution. The data points are represented on the side of the average. It is used in the field of statistics.

Skewed Distribution

Skewed Distribution is a type of distribution that is asymmetrical in nature, which naturally resists end results on one side. It is used for analyses of a product that is unadulterated.

Multimodal Distribution

Multimodal distribution, also known as plateau distribution, is used for many peak adjacent tips of the distribution.

Edge Peak Distribution

Edge Peak Distribution is similar to the normal distribution except that it possesses a bigger peak at one tail. It is combined with data and represented as named “greater than”.

Dog Food Distribution

Dog Food Distribution involves results that are close to the average. In this, if an end-user will receive this distribution, then some others will receive a heart cut distribution.

• The other end-user who is left will get dog food where the ends and odds are left after the meal of the master.
• It will create an end user process.

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Difference between Histogram and Bar Chart

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There are some main points of differences to be remembered between a histogram and a bar chart. Let us look in detail. 

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Things to Remember 

• A histogram is the graphical representation of data where data is grouped in bars of different heights, also called bins. 
• The data is continuous here, unlike bar charts.
• Histograms deal with quantitative data which is continuous. 
• Based on their nature, a histogram has been divided into different heads.
• Various parts of a histogram are equally important in its work.
• A histogram observes continuous data, whereas in a bar chart, gaps are present between the bars. 

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