### Table of contents

### A Guide to Six Sigma Statistics

Statistics are the foundation of Lean Six SigmaSix Sigma Definition: Six Sigma is a set of techniques and t... Learn More... projects. This allows us to express the data that makes up X and Y using numbers. A Six SigmaSix Sigma Definition: Six Sigma is a set of techniques and t... Learn More... StatisticA Sample Statistic, and a Population Parameter A sample for... Learn More... is an integral part of every organization’s day-to-day operations. Six Sigma projects are based on numbers, diagrams, and data. Six Sigma professionals and all stakeholders need to be familiar with basic LeanLEAN Definition LEAN is a production method aimed primarily ... Learn More... Six Sigma statistics and statistical analysis.

### Types of Data in Six Sigma

Data can be either quantitative or qualitative. It could be a number or a measurement.

**Qualitative**: This data is also called non-numeric and describes the characteristics of a value. Each data point can be placed in one of several possible categories.

Different types of qualitative data

**Nominal DataSix Sigma uses nominal data, which is categorical informatio... Learn More...:**This type of descriptive data can be used to refer to the names and labels of data points. For example, hair color could be black or brown, and gender could be male or female.**Ordinal Data:**Oral data gives good information about the order in which choices are made. It arranges information in a certain order but does not indicate a relationship between items. Ex: Pass or fail, customer service good or bad, etc.

**Quantitative Data:** Also known as **numerical data**. Data points can be either measured or counted. It is not like Qualitative data because it can contain infinite numbers of possible categories in which each data point could be placed. Quantitative data can be further subdivided into two types of data:

**Distinct data**: Data is considered discrete when the numbers or counts are whole numbers. You could use this data to determine customer complaints and weekly defectsMuda (無駄, on'yomi reading) is a ... Learn More....**Continuous dataContinuous data is a type of data that can take on any value... Learn More...**: The data is continuous when the measurement takes on any value. Usually, this rangeIn statistics, the range of a set of data is the differenc... Learn More... is within a certain range. For example, Stack height, distance, cycle timeThe cycle time is the time it takes to produce an item or pr... Learn More..., etc.

### Basic Types of Lean Six Sigma Statistics

The statistic in Six Sigma is based on principles and methods for gathering, analyzing, interpreting, and communicating data in meaningful ways. Statistics can help you understand data behavior and identify improvement opportunities.

Types of statistical analysis

#### Descriptive statistics

These values describe the characteristics of the population or sample. It is a summary of the measures and the sample.

#### Central Tendency

The statistical measure is used to find the center of data distributionUsed for determining the confidence interval for means or fo... Learn More... in six sigma statistical analysis. Based on the circumstances, the measure central tendency could either be Mean, MedianIn statistics and probability theory, the median is the... Learn More..., or ModeThe mode is the value that appears most often in a set of ... Learn More....

- The means The sum of all data values divided by the number of data points is called the mean.
**Median**The median value is the averageA synonym for “mean”: the sum of a set of values divided... Learn More... value of the data when it is ordered from least to most or vice versa. If there are even data values, the median will be the average of those two values.**Mode**This is the value that most often appears in the data set.

#### Dispersion measurement

The degree of variation in data is called dispersionDispersion Dispersion refers to the spreading or scattering ... Learn More.... Dispersion is the degree to which items disperse from the central tendencyThe Measures and definitions for central tendency allow you ... Learn More....

Different measures of dispersion

Range The Range refers to the difference between the maximum value and the minimum.

Variance is a measure of the dispersion between data points that are close to their mean value.

Standard Deviation is the most common measure of dispersion. It measures the variation in a processThere are many ways to organize your lean six sigma processe.... Standard DeviationCumulative probability of a normal distribution with expecte... Learn More... (or standard deviation) is one of the most commonly used measures of variability within a population or data set.

Kurtosis: Kurtosis can be used to determine if the data is heavier-tailed than a normal distribution. It is simply a measurement of the tails in a distribution.

#### Inferential statistics

Inferential lean six sigma statistics are used to draw inferences or conclusions about the traits of a population using data from a sample. This is also known as using probability to infer population parameters from data collected in a sample. T-tests, Regression analysis, and Analysis of variance (ANOVA)An analysis tool in statistics called Analysis of Variance (... Learn More... are just a few examples.

#### Distribution

The form of data distribution can be characterized by its number and symmetry possession. Skewness refers to the absence of symmetry. Skewness, in other words, is the degree to which the probability distribution for a random variable differs from the Normal Delivery.

**Symmetrical distribution**: A symmetrical distribution is generally a bell curve. The perfect normal distribution is the probability distribution with zero skewness. Symmetrical distribution is when the mean, median, or mode are at the same place, and the values for data points occur at regular frequencies.

**Positively Skewed Distribution:** A distribution is said to be skewed towards the right if its tail leads toward the right. A positively skewed distribution has a skewness greater than zero.

**A Negatively Skewed Distribution:** If a distribution has a long tail that leads to the left, it is considered to be skewed towards the left. A negatively skewed distribution has a skewness of less than zero.

### Six Sigma Tree Diagram

Six Sigma Tree diagrams are an analytical and planning tool that helps to divide larger problems into smaller pieces. You can also call it a systematic diagram, hierarchy diagram, or analytical tree. It is one of seven management tools for six sigma statistical analysis. These tools can be used to plan and manage operations efficiently. 7M tools are designed to help managers plan, analyze, and make decisions.

The six sigma Tree diagram is a way to break down complex concepts into smaller pieces. This six sigma diagram is designed to help you break down concepts into their constituent parts.

The six sigma tree diagram begins with one item and branches into several more. Another branch can be split into more branches. It looks almost like a tree with multiple branches and a trunk.

#### How to make a Tree Diagram

- The goal statement for the project or problem should be determined. The goal should be placed on the left or top of the diagram, depending on whether it is a horizontal or vertical tree.
- Identify the key tasks and subtasks that must be completed to reach your project goal.
- You should brainstorm all possible solutions for each task or subtask. This diagram should be used to move from general to more specific.
- Verify each item and identify additional tasks needed to reach the goal.
- Keep going until you reach the basic elements. Continue the exercise until you exhaust all options.

### The data in a bite

**Graphical Analysis** is a great way, to sum up, the data in Six Sigma Statistic projects. The graphical analysis takes the data and creates images that help to understand the relationships between the process parameters. Graphical analysis is often the first step in any problem-solving process.

Different methods of graphic analysis:

**Box and Whisker plotHow do box plots work? Box plots make it easy to visualize t... Learn More...** is also known as Box and Whisker plot. It is a pictorial representation of continuous data. The box plotHow do box plots work? Box plots make it easy to visualize t... Learn More... displays the Max, Min, and median values, as well as the interquartile range Q1, Q3, and outlier.

A **time seriesWhat is a Time Plot? A time plot, also known as a time serie... Learn More... plot** is a line graph that plots data over time. It allows you to see the patterns in the time series. They don’t have control limitsA control limit chart definition is made up of many parts.&n... Learn More... so we can’t judge if the process is stable.

A **histogram** shows a graphic representation of a frequency distribution. It’s rectangular with the class intervals being the bases and the frequencies as the heights. There is no space between the two rectangles that follow it.

**Pareto ChartPareto chart analysis can be used to make business decisions... Learn More...** also known as the **80-20 Rule**. It is a combination bar chartBar charts are stacked to allow you to show data values as v... Learn More... and a line chart. The actual data are in descending order with a bar chartBar charts are stacked to allow you to show data values as v... Learn More... and the cumulative data are in ascending order with a line graph.

#### Six Sigma Statistic Data Symbols

**s or sd:** This sample standard deviation represents a point estimate of the population standard deviation/the dispersion statistics for samples

**u** – The central tendency statistics for people

**XBar** – A point estimate of the population meanA synonym for “mean”: the sum of a set of values divided... Learn More...

**s** – The actual population standard deviation/symbol to measure dispersion within a population

**N** – refers to populations

**n** – This is the statistic for how much data are in a sample

**x** – the individual value

#### Do you have any tips and tricks for someone who’s learning about statistics in Lean Six Sigma?

Leave them in a comment down below.