# Statistical Analysis Tools in Six Sigma - Histogram

## What is a Histogram?

Histograms are graphical representations that display the distribution of data. They help Six Sigma practitioners to understand the variation present in a process. Histograms plot the data in bar-like structures. They provide insights into the central tendency, shape, and spread of the data. For example, imagine a manufacturing company that wants to analyze the distribution of product defects across different shifts. With a histogram, they can visualize which shifts have the most common defects, enabling targeted improvement efforts.

## How to create a Histogram?

The construction of a histogram involves the following steps:

#### Determine the range of values:

First, identify the minimum and maximum values in the dataset.

#### Decide the number of bins:

Next, select the appropriate number of intervals or bins to divide the range of values. This choice affects the level of detail and smoothness in the histogram. However, too few bins can oversimplify the distribution, while too many bins can obscure patterns.

#### Calculate bin width:

Next, divide the range of values by the number of bins to determine the width of each bin.

#### Count the frequency:

Then, count how many data points fall within each bin.

#### Plot the histogram:

Finally, drawbars for each bin, with the width representing the bin width and the height representing the frequency or count.

Histograms are used in various fields such as statistics, data analysis, and data visualization. They are specifically used to explore and understand data distributions, identify outliers, detect patterns, and make data-driven decisions.

## Example:

## How to interpret a Histogram?

#### Understand the Axes:

- The horizontal axis (X-axis) represents the range of values in our dataset, divided into intervals or bins.
- The vertical axis (Y-axis) represents the frequency or count of data points falling into each bin.

#### Analyze the Shape:

- Observe the overall shape of the histogram. Common shapes include:
**Symmetric**: The data is evenly distributed around a central value, forming a bell-shaped curve. This indicates a normal distribution.**Skewed**: The data is concentrated on one side, causing the histogram to be asymmetric. It can be either positively skewed (tail to the right) or negatively skewed (tail to the left).**Bimodal**: The data has two distinct peaks, suggesting two separate subgroups within the data.**Uniform**: The data is evenly distributed across all bins, indicating a uniform distribution.

- Observe the overall shape of the histogram. Common shapes include:
#### Identify Central Tendency:

- Look for the central tendency of the data, such as the mean, median, or mode. In a symmetric histogram, these measures should be close together.

#### Check for Spread and Variability:

- Assess the spread or variability of the data. A wide histogram indicates high variability, while a narrow one suggests low variability.

#### Detect Outliers:

- Outliers are extreme values that fall far away from the majority of the data. These are points that lie outside the typical distribution and may require special attention.

#### Consider the Context:

- Always keep the context of your problem or project in mind. Understanding the histogram will be more meaningful when we relate it to our specific objectives.

#### Make Data-Driven Decisions:

- Use the insights gained from the histogram to drive data-driven decisions. It helps to identify potential areas for improvement and where to focus our efforts to achieve process excellence.

## When to use a Histogram?

Histograms are useful in various scenarios where you need to understand the distribution and frequency of data values. Here are some situations where you can use histograms:

#### Data Exploration:

Histograms give you a clear picture of the data spread, visually showing you the distribution of values. With histograms, you can spot interesting patterns, and outliers, and see the values scattered across the range. This initial exploration is essential because it sets the foundation for a deeper analysis. This further helps you to gain valuable insights and a better understanding of the data’s underlying patterns and characteristics.

#### Descriptive Statistics:

Histograms help in summarizing and visualizing the central tendency and variability of data. In addition, they provide information about the mode (most frequent value), median (middle value), and skewness (asymmetry) of the distribution.

#### Data Preprocessing:

Histograms help in the data preprocessing step to transform skewed data or identify data points that may need further investigation. Further, they can assist in deciding on appropriate data transformations, such as log transformations, to achieve a more normalized distribution.

#### Feature Selection:

Histograms aid in feature selection tasks by analyzing the distribution of features in relation to the target variable. Additionally, they help identify features that exhibit significant variation or have a strong correlation with the outcome of interest.

#### Outlier Detection:

Histograms highlight potential outliers by revealing data points that fall outside the expected range or show an unusual frequency. Consequently, outliers are identified as values that appear as individual bars or lie far away from the bulk of the distribution.

#### Hypothesis Testing:

For hypothesis testing, histograms are useful in testing scenarios, such as comparing two groups or assessing the goodness of fit between observed and expected distributions. In addition, they allow you to visually compare the distributions and evaluate the significance of differences.

#### Process Monitoring:

Finally, histograms play a role in process monitoring and control. By tracking the distribution of process measurements or outcomes over time, histograms can signal shifts or changes in the process that may require attention or investigation.

### Summary

In summary, it is important to note that histograms are best suited for continuous or discrete data with a relatively large number of observations. Furthermore, they provide a visual representation of the data distribution and are particularly effective in revealing patterns and insights that may not be apparent from raw data alone.