﻿ Basic Statistics
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# Intro to Basic Statistics

Basic Statistics or statistics is the science of collection, analysis, interpretation and presentation of data.

In Six Sigma, we apply statistical methods and principles to quantitatively measure and analyze process performance and process improvements. We use facts, information and empirical evidence to reach conclusions and solve business problems. Statistical analysis enables factual & quantification elements of any population or set of measures to be evaluated.

### Types of Statistics

• Descriptive Statistics
• Inferential Statistics

### Descriptive Statistics

Descriptive statistics are in fact basic statistics. Descriptive statistics are applied to describe the main characteristics of a collection of data. They summarize the features of the data in a quantitative manner.

Descriptive statistics are descriptive only and they do not make any generalizations beyond the data at hand. Data used for descriptive statistics are for the purpose of representing or reporting.

### Inferential Statistics

Inferential statistics are applied to infer the characteristics or relationships of the populations from which the data are collected. Inferential statistics draw statistical conclusions about the population by analyzing sample data.

Any complete data analysis includes both descriptive statistics and inferential statistics.

### Statistics vs. Parameters

The word "statistic" refers to a numeric measurement calculated using a sample data set. For example, sample mean or sample standard deviation. Its plural is "statistics" (same spelling as "statistics" which refers to the science discipline).

The parameter refers to a numeric metric describing the population, for example, population mean and population standard deviation. Unless you have the full set data of the population, you won't be able to know the population parameters.

### Continuous vs. Discrete Data

Continuous Variable's are measured. There are an infinite number of values possible. Examples might include

• Temperature
• Height
• Weight
• Money

Discrete variables are counted. There are a finite number of values available. Examples might include

• Count of defects
• Count of defectives
• Count of products with certain characteristics (color, state etc.)

### Types of Data

There are a few different types of data that you should realize and understand before we get any deeper into the statistics of Six Sigma.

• Nominal: Categorical data; colors, states etc.
• Ordinal: Rank ordered data; first or second place in race, scores of exams etc.
• Interval: Equidistant data; temperature with Fahrenheit or Celsius scale.
• Ratio: Numbers that can be measured on a scale ratio and be compared as multiples of on another; weight, length, elapsed time etc.

Interval and Ratio data are forms of continuous data and are quantifiable. Nominal and ordinal data are forms of discrete data because they are categorical and finite.

With this intro & primer we can now move onto a more complete review of basic statistics. The next lesson is Descriptive Statistics where we will explore how to understand and quantify data shape, location & spread.