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# Histogram|Definition & Meaning

## Definition

A **frequency** distribution displays how many times each **value** in a set of data occurs. The most **widely** utilized graph to **display** frequency distributions is a **histogram.**

In statistics, a **graphical** representation of the dispersal of data is a **histogram.** The histogram is defined by a set of **rectangles,** bordering each other, where each bar or rectangle **represents** a kind of **data. **

Figure 1 – Depiction of Histogram

**Statistics** is a kind of mathematics that is applied in different **fields.** When numerals are **duplicated** in statistical data, this **duplication** is known as **Frequency** and it can also be shown as a table, called a **frequency** distribution. A Frequency **distribution** can be displayed graphically by the different types of **graphs;** a Histogram is among them.

## What Is a Histogram?

A histogram **represents** grouped frequency distribution with **continuous** classes in a graph form. The **histogram** is an area diagram that can be **described** as a bunch of rectangles with bases **alongside** the intervals between class **boundaries** and with areas related to **frequencies** in the related classes. In these representations, all the **rectangles** are joined and there is no space between them because the base **coats** the intervals between class **boundaries.** The heights of **rectangles** are related to corresponding **frequencies** of similar classes and for different **classes** so the **heights** will be dependent on **frequency** densities.

In **Histogram** data is represented into **continuous** number ranges and each range is related to a **vertical** bar. The horizontal or X axis shows the number range. And the **vertical** or Y axis (frequency) represents the **density** of data which is present in given range. The number **ranges** relay upon the data that is being used.

## How To Plot Histogram?

You need to **follow** the given steps to make a **histogram.**

- First of all, on the
**X-axis,**plot the class intervals, and on the**Y-axis**plot**frequencies.** - Both axes
**should**have the same scale. - Class intervals are
**required**to be exclusive. - Now plot
**rectangles**with their base as class intervals and the**base’s**frequencies as**heights.** - Each
**rectangle**is based on its respective class**interval**because the class limits are**marked**on the horizontal axis, and the**frequencies**are marked on the**vertical**axis. - The
**height**of each rectangle is related to the**corresponding**class frequency when the**intervals**are equal. - The
**area**of every individual rectangle is related to the**affiliated**class frequency when the**intervals**are unequal.

In figure 1, **Histogram** is made using the below data.

On the **x-axis** is the range of weights of **students** from 55 to 90 with 7 **rectangular** bins and on the y-axis is the **frequency** or how many students have the **weight** in the particular range.

## When To Use a Histogram

Use a histogram when:

- The
**data**is in numerical form. - When
**determining**whether the output of a process is**distributed**normally or not, you**should**notice the shape of the data’s**distribution.** - To
**analyze**whether a specific**process**can meet the customer’s requirements - To
**analyze**what the output from a supplier’s**process**will look like. - To see whether a
**process**change has happened from one time**span**to another. - To
**determine**if two or more processes have the same**output**or not. - You want to
**communicate**the distribution of data through**graphical**representation**quickly**and easily to others.

## Difference Between Bar Graph and Histogram

A **histogram** is one of the most widely used graphs to **present** the frequency distribution. As we know that the **frequency** distribution shows the amount of each **different** value occurring in the data set. The **histogram** looks much similar to the bar graph, but there are **differences** between them.

### Histogram

The **histograms** are two-dimensional graphs. The **frequency** or density in the histogram is shown by each **rectangle’s** area. Also in histograms, the rectangles are in contact with each other since their bases are **ranges.**

### Bar Graph

Bar Graphs are **one-dimensional** graphs. The height of a rectangle in a Bar Graph represents the number of **happenings** and the width has no such importance. In bar **graphs,** rectangles are isolated and have equal **spaces** in between them meaning their bases are not **connected.**

## Types of Histogram

The **histogram** is to be classified into **different** types on the basis of the frequency **distribution** of the data. There are **various** types of distributions, which are normal **distribution,** multimodal distribution, **bimodal** distribution, comb distribution, dog food **distribution,** edge peak distribution, and so on. The **histogram** can be used to represent the **above-mentioned** types of distributions. The different types of a **histogram** are:

### Uniform Histogram

A **uniform** distribution shows that the number of **classes** is a very small number, and each class also has the **exact** same number of happenings. It may include a **distribution** that might have **several** peaks.

### Symmetric Histogram

The **symmetric** histogram is also known as a **bell-shaped** histogram. When you cut the **histogram** from the **center** creating two equal parts to it, and the two parts are **identical** in size and shape, the **histogram** is called a **symmetric histogram.** The right half portion of the image **should** be the same as the left half in order for the diagram to be perfectly **symmetric.** The histograms that are not symmetrical are known as **skewed.**

### Bimodal Histogram

In the event that a **histogram** contains two peaks, it is **called** a bimodal. **Bimodality** happens **when** the data set has observances on two **different** kinds of combined groups or **individuals** and if the centers of the two **separate histograms** are too far from the variability in both the **data** sets.

### Probability Histogram

A **Probability** Histogram shows a **graphical** representation of a discrete **probability** distribution. It has rectangles that are **centered** on all the values of x, and also the **area** of every rectangle is related to the **value** of the probability of the corresponding value. The **probability** histogram **diagram** is drawn by first selecting the **classes.** The probabilities of each outcome **determine** the heights of the bars of the **histogram.**

## Application of Histogram: Normal Distribution

The **typical** shape that looks just like a **bell curve** is phrased as a **normal** distribution. In this, The **majority** of the data points emerge on the flank of the **mean** as on the other. It is to be mentioned that other **distributions** occur identically to the **normal** distribution.

The **computations** in statistics are used to ascertain a **distribution** that is a normal **distribution.** It is needed to notice that the phrase **“normal”** describes the specific **distribution** of a methodology. For **example,** in many methods, normal **distribution** retains a natural limit on a flank and forms skewed **distributions.** The normal in this represents the **procedures,** in the scenario where the **distribution** is not regarded as **normal.**

## Histogram Example

Make a **Histogram** of the following data.

Figure 3 – Customers and waiting time data.

### Solution

The **histogram** of the **given** data is plotted below:

Figure 4 – Histogram of the customer and waiting time data

*All images/mathematical drawings were created with GeoGebra.*