## Histogram

Histogram is a graphical representation of the distribution of numerical data. It is an estimate of the probability distribution of a continuous variable (quantitative variable) and was first introduced by Karl Pearson. It is a type of bar chart where the width of the bars are equal to the class interval, and the height represents the frequency. The frequency is the number of times that observation occurs in a given class interval.

It is an accurate representation of the distribution of data that can be used to find outliers and skewness in the data. The histogram can be used to find the range, mean, median, and mode of the data.

### Example of Histogram

An Example of a Histogram would be: if you have data on the heights of students in your class, you could make a histogram to show how many students are at each height. To make a histogram, you first need to decide what values to use for the x-axis and y-axis. The x-axis is usually the value that you are measuring, and the y-axis is the number of times that value occurs.

For example, if you are measuring the heights of students in your class, you would use heights for the x-axis and the number of students at each height for the y-axis.

Once you have decided what values to use for the x-axis and y-axis, you can plot your data. There are a couple of ways you can do to make a histogram.

### Parts of Histogram

There are three parts to a histogram:

- The Bars
- The Axis
- The Labels

#### The Bars

The bars of a histogram represent the frequency of occurrence for each value. The height of each bar corresponds to the number of times that value occurs.

#### The Axis

The axis is the horizontal line that goes across the bottom of the histogram. The axis is divided into equal intervals, and each interval represents a different value.

#### The Labels

The labels are the numbers that appear on the axis. They indicate what each interval represents in terms of the data values.

### Types of Histogram

There are four types of Histogram:

- Uniform histogram
- Symmetric histogram
- Bimodal histogram
- Probability histogram

#### Uniform Histogram

Uniform histogram is a graphical representation of data that looks like a bar chart, but with the bars evenly spaced out. The purpose of a uniform histogram is to show how data is distributed across a range of values.

#### Symmetric Histogram

A symmetric histogram is a graphical representation of data that is mirror-symmetric about a line of reflection. The line of reflection can be either horizontal or vertical. A histogram is a graphical representation of data that shows the frequency, or a number of times, that a certain value occurs.

#### Bimodal Histogram

A bimodal histogram is a type of graph that shows two distinct peaks. This indicates that there are two different groups of data. Bimodal histograms are often used to compare data sets.

#### Probability Histogram

A probability histogram is a graphical representation of a probability distribution. It is a type of bar chart that shows the probability of each possible outcome. The height of each bar represents the probability of that outcome occurring.

### How to Plot Histogram

The following steps can be used to plot a histogram:

- Choose the appropriate bin size. The bin size should be chosen so that it is large enough to accurately represent the data, but not so large that it loses resolution.
- Determine the range of values for each bin.
- Count the number of data points that fall within each bin.
- Plot the bins on a graph, with the height of each bin representing the number of data points in that bin.
- Connect the tops of each bin together. This creates a line that represents the frequency density function.
- Plot the midpoint of each bin on the x axis. This creates a line that represents the relative frequency function.
- The area under the frequency distribution function represents the probability of a data point being in each bin.

#### How to make Histogram in Excel

Excel has a built-in feature that allows you to create histograms from your data.

- First, select your data.
- Then click on the Insert tab and choose Histogram from the charts menu.
- A dialog box will appear asking you to select your data and bin ranges.
- Once you have selected your options, click OK and your histogram will appear!

### When to use Histogram

There are a few different situations where a histogram can be used:

**-To compare data sets:**

Histograms can be used to compare two or more data sets. This is especially helpful when the data sets are large and have multiple variables.

**-To find outliers:**

Histograms can help you identify outliers in your data set. Outliers are values that are far from the rest of the data.

**-To see the distribution of data:**

A histogram can help you see how your data is distributed. This is helpful for understanding variance within a data set.

### Purpose of Histogram

The purpose of a histogram is to help you understand the distribution of data. It can be used to show the distribution of data in a number of ways. One way is to show the distribution of data by class interval. For example, if you have data that is grouped into intervals, you can use a histogram to see how many times each value occurs. Another way to use a histogram is to show the distribution of data by frequency. For example, if you have data that is not grouped into intervals, you can use a histogram to see how many times each value occurs.

#### Advantages of Histogram

Some Advantages of Histogram are:

- They make it easy to see the shape of the distribution of data.
- They can be used to find out whether the data is symmetrical or skewed.
- They can be used to find out whether there are outliers in the data.

#### Limitations of Histogram

Some Limitations of Histogram are:

- Histograms can only be used for numerical data. This means that if you have non-numerical data, you will not be able to create a histogram.
- They can only be used for interval or ratio data. This means that if you have ordinal data, you will not be able to create a histogram.