Histogram

 

Histogram

In statistics, a histogram is a graphical representation of the distribution of data. The histogram is represented by a set of rectangles, adjacent to each other, where each bar represent a kind of data. 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 a 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, a histogram is a diagram involving rectangles whose area is proportional to the frequency of a variable and width is equal to the class interval.

How to Plot 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.

Comments

Post a Comment

Popular posts from this blog

BODMAS RULE IN MATHEMATICS

Image
  What is BODMAS ? The evaluation of an expression involving numbers is one of the basic tasks in arithmetic. If an expression contains addition (+), subtraction (-), multiplication (x), division (÷), bracket (), and Of (of), then the precedence of simplification of the operation is given by “BODMAS rule”. First, we have to know that what is  BODMAS rule ? Or What is BODMAS formula? BODMAS rule  is a rule or order that is used to simplify the arithmetic expression involving more operators in mathematics. When an equation involving more operators first we have to know that in which order we have to solve the expression. This problem is solved with the help of BODMAS rule. The full form of BODMAS is: B rackets (Parts of a calculation inside the bracket always come first). Precedence of brackets are : [{(bar)}] O rders (powers and square roots) D ivision M ultiplication A ddition S ubtraction Each letter of the word stands for the first letter of an operator. If an expressio...
Read more
Image
Pascal's Triangle Pascal’s Triangle  is a kind of number pattern.  Pascal’s Triangle is the triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression.  The numbers are so arranged that they reflect as a triangle. Firstly, 1 is placed at the top, and then we start putting the numbers in a triangular pattern. The numbers which we get in each step are the addition of the above two numbers. It is similar to the concept of  triangular numbers .  In this article, we are going to learn Pascal’s triangle history, definition, properties, patterns, formulas and examples with complete explanation. Table of contents: History Definition Construction How to use Patterns Properties Formula Expansion FAQs Pascal’s Triangle History Blaise Pascal was born at Clermont-Ferrand, in the Auvergne region of France on June 19, 1623. In 1653 he wrote the Treatise on the Arithmetical Triangle which today is known as the  Pascal’s Triang...
Read more

History of Statistics

 The early writings on statistical inference date back to Arab mathematicians and cryptographers, during the Islamic Golden Age between the 8th and 13th centuries. Al-Khalil (717–786) wrote the Book of Cryptographic Messages, which contains the first use of permutations and combinations, to list all possible Arabic words with and without vowels.[13] In his book, Manuscript on Deciphering Cryptographic Messages, Al-Kindi gave a detailed description of how to use frequency analysis to decipher encrypted messages. Al-Kindi also made the earliest known use of statistical inference, while he and later Arab cryptographers developed the early statistical methods for decoding encrypted messages. Ibn Adlan (1187–1268) later made an important contribution, on the use of sample size in frequency analysis.[13] The earliest European writing on statistics dates back to 1663, with the publication of Natural and Political Observations upon the Bills of Mortality by John Graunt.[14] Early applicati...
Read more