What is a Histogram in MATLAB?

Histogram in Matlab is a fundamental Data Visualisation tool widely used across various fields. Imagine you have a jar filled with different coloured marbles. A MATLAB Histogram would be like sorting those marbles into distinct piles based on their colour. Then, showing you how many marbles are in each pile.

This visual representation of the data distribution provides valuable insights that can inform your analysis. Additionally, you can achieve decision-making benefits from these representations. Dive in deeper to learn more about MATLAB Histograms.

Table of Contents 

1) A Brief Introduction to a Histogram in Matlab

2) Components of a Histogram in MATLAB 

3) Types of Histogram Distributions in Matlab

4) Plotting a Histogram in MATLAB 

5) Conclusion 

A Brief Introduction to a Histogram in Matlab

Histograms are a form of a bar plot specifically for numerical data. The properties of a Histogram can be modified by adjusting the values of its properties. Changing the values is useful for quickly modifying the bin properties or displaying changes. For a more in-depth exploration of Histogram-related operations, including techniques like Matlab Convolation for advanced data analysis, MATLAB provides a versatile platform to adapt and customise these visualisations according to your specific needs.

Histograms are of various shapes: 

1) Bell-shaped 

2) Skewed right 

3) Skewed left 

4) Bimodal 

5) Random 

Discrete or continuous forms of data can be summarised using Histograms. Although quite like a vertical bar graph, a Histogram has no gaps between the bars.


 

Components of a Histogram in MATLAB 

Here are the components of MATLAB Histogram: 

1) Title: The title is a short description of the Histogram's information. 

2) X-axis: The X-axis displays the intervals which show the value scales under which the measurements fall. 

3) Y-axis: The Y-axis displays the number of times the values have occurred inside the interval bins set by the X-axis. 

4) Bars: The height of each bar shows the number of times the values have occurred inside the intervals. The width of each bar shows the interval which is covered. In the case of a Histogram with equal-sized bins, the width will be consistent across all the bars. 

Types of Histogram distributions in MATLAB

When a user creates a Histogram, a visual representation of the data distribution is generated. Histograms can display large volumes of data and the frequencies of the data values. A Histogram can help a user determine the median and distribution of data and display any outliers in the data. Here are descriptions of key distribution types:

1) Normal Distribution: A Normal Distribution illustrates how the points on one side of the average value are also likely to occur on the other side of the average.  

2) Bimodal Distribution: This type of distribution has two peaks, where the data is separated and then analysed as two separate normal distributions. 

3) Right-skewed Distribution: A Right-skewed Distribution is also referred to as a positively skewed distribution. In this distribution, there are many data values on the left side compared to fewer data values on the right side. This type of distribution typically occurs when the data has a range threshold on the Histogram’s left side. 

4) Left-skewed Distribution: This distribution type is also called a negatively skewed distribution. Left-skewed distributions display many data values on the right side compared to the number of values on the left side. This distribution typically occurs when the data has a threshold range on the Histogram's right side. 

5) Random Distribution: Random Distributions generally lack apparent patterns and contain many data peaks. In this distribution type, various data properties can be combined. Hence, it is recommended to separate the data and then analyse it. 

6) Comb Distribution: Comb Distributions comprise bars shown alternatively by tall and short heights. These bars result from data that is rounded off or an incorrect Histogram. For example, if a temperature value is rounded off to the nearest 0.2 degrees, the bar shape would be displayed as a comb if the bar’s width is 0.1 degrees.   

7) Edge Peak Distribution: This distribution is similar to the normal distribution, except it has a higher peak at one of the tails. This occurs because of an incorrect construction of the Histogram. 

Plotting a Histogram in MATLAB 

The MATLAB software uses the built-in function ‘hist()’, which allows users to plot a bar graph. The basic syntax of the function to plot a Histogram is Histogram(X). The variable ‘X’ represents the data and is a vector form. 

The Histogram(X) function utilises an automatic binning algorithm which returns multiple bins of equal width. Additionally, these bins are also spread out according to the data stored in the vector ‘X’. The function also reveals the underlying distribution shape to the user. The bins are displayed in MATLAB as rectangles whose height indicates the number of elements inside the bin. 

One use of the Histogram function is: Histogram(X, nbins)  

This variation uses the exact number of bins specified by the variable ‘nbins’. ‘Nbins’ is a positive integer value. If this value is not specified, the Histogram automatically calculates the number of bins to display depending on the values in the vector ‘X’.  

A MATLAB Histogram can also be saved with the ‘savefig()’ function. It can be loaded into the workspace again with the ‘openfig()’ function. 

Example of a Histogram Plot in Matlab

Here is a code to plot a simple Histogram in MATLAB: 
 
The above code will generate 10000 random numbers with the function histogram(). According to the binning algorithm, this code will automatically generate the appropriate number of bins.


 

Conclusion

A Histogram in MATLAB is typically a graphical representation of data. It is plotted using MATLAB's Histogram() function and allows users to create bar graphs for any vector or matrix. Histograms utilise the automatic binning algorithm for grouping the data into bins. More importantly, they are most beneficial for analysing large datasets, patterns and outlier identification. 

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