# Histogram

Histogram — a visual representation of tabular information in the form of column diagrams. The quantitative ratios of various indicators are represented by the rectangles with a proportional area. The histogram displays the distribution of individual measurements in a parameter or process.

## Drawing of Histogram

Visually the histogram resembles the range of rectangular cuboids located on the coordinate axis. A horizontal axis (X-axis) demonstrates the number range. A vertical axis (Y-axis) displays the number of data in each range. Figures fit snugly to each other.

Each bar represents a numeric value which is called a bin (bucket). A high of the bar shows the frequency of measuring points with a value within the corresponding bin.

The creation of a histogram has an order which is necessary to follow. The main things for an accurate histogram are the qualitative measurement of the data and the proper use of visual methods.

**Stages of histogram’s drawing:**

- Measure the necessary parameters and collect the statistical data. It is better to have several measurement results to make the representation of data more illustrative.
- Identify the highest and smallest value of the indicator among the calculated measurement results.
- Define the width of the indicator values, and subtract the smallest value from the biggest one.
- Select the proper number of intervals within which it is necessary to group the results of measurements.
- Define the limits of intervals. The limits of the intervals should be fixed in such a way that data values don’t fall into any boundary of the interval.
- Calculate how many times the value of the measurement results fell into each interval.
- Draw up a histogram. Mark the intervals on the abscissa axis (horizontal axis) and indicate the frequency of measurement results in each interval on the ordinate axis (vertical axis). As a result, you will see a column diagram (histogram).

## Application of the Histogram

The histogram is a perfect way to represent the dynamics of a production process. It provides the possibility to display the changes in the measured parameters of the object and visually evaluate the law of their distribution. The histogram is used to analyze stability and accuracy in various processes and for quality management.

**Cases when it is necessary to use a histogram:**

- Comparison of the numeric data;
- Overseeing the data distribution of the standard process.
- Identification of whether the product meets the client’s demand.
- Analysis of the performance from a supplier’s process.
- Defining the periodicity in a certain process.
- Defining the similarities and differences of the process in various periods.
- Identification of differences between the results of two or more processes.

## Types of Histograms

There are several types of histograms. Let’s look at them in detail.

**Normal **

This pattern is known as the typical distribution. Visually it looks like a mountain-shaped curve with equal symmetrical sides. Usually, this histogram represents the typical process. However, it is necessary to remember that a typical process doesn’t mean a normal one.

**Skewed **

This pattern is non-symmetrical because it shows the prevailing number of certain results. It looks like a mountain whose peak is skewed on the right or left side.

**Double-Peaked **

Such a histogram looks like two humps of a camel. The histogram displays two combined processes. This situation happens if the measurement results are obtained from two different sources.

**Multimodal (Plateau)**

On this histogram, the peaks are located close to each other. The top of the pattern looks like a plateau. This situation occurs when several processes with standard distribution are put together.

**Edge Peak **

Here the chart has one large peak and a small tail. It happens when the data are collected into the group “bigger than”.

**Comb **

This histogram resembles the chart with long and short bars. This distribution appears when the data are adjusted, or the histogram is created incorrectly.

**Heart-Cut **

This chart resembles the normal distribution without tails. Truncated distribution appears, then the possibility to record the data is limited.

**Dog Food **

This pattern is called dog food because the chart resembles the distribution of hound food: the buyer has received the “leftovers” from the food of someone else.

## Differences between the Histogram and bar chart

The bar chart is a practical way to visually represent a certain amount of data. The bar chart is often confused with the histogram, but they have some different traits.

**Comparison of Histogram and bar chart:**

**Histogram **

- Bars represent the frequency of certain data.
- Bars show the non-discrete variables.
- No space between bars.
- Bars can’t be reordered.
- Width of bars can be different.
- Data on the quantity.
- Visual pattern.

**Bar chart**

- Bar chart helps to compare the different categories.
- Bars show the discrete variables.
- Space between bars.
- Bars can be reordered.
- Width of bars should be different.
- Data on the categories.
- Visual pattern.