## Shop Essentials (Applied Mathematics) Training

Class Information
 Tooling U-SME classes are offered at the beginner, intermediate, and advanced levels. The typical class consists of 12 to 25 lessons and will take approximately one hour to complete.
 Class Name: Statistics 220 Description: This class covers the main concepts of statistics and relates these concepts to shop situations. Difficulty: Intermediate Number of Lessons: 18 Language: English, Spanish, Chinese

Class Outline
• Objectives
• What Is Statistics?
• What Is Variation?
• Natural vs. Unnatural Variation
• Why Use Statistics?
• Probability and Sampling
• Mean
• Types of Mean
• Median and Mode
• The Histogram
• The Bell-Shaped Curve
• Types of Bell-Shaped Curves
• Range
• Standard Deviation
• Standard Deviation and the Bell-Shaped Curve
• Standard Deviation: An Example
• Random Sampling
• Summary

Class Objectives
• Define statistics.
• Explain how variation appears in a shop.
• Distinguish between natural and unnatural variation.
• Describe common uses for statistics.
• Define probability.
• Calculate the mean for a set of numbers.
• Distinguish between a population mean and sample mean.
• Calculate the median for a set of numbers.
• Calculate the mode for a set of numbers.
• Describe the information contained in a histogram.
• Describe the appearance of a bell-shaped curve.
• Describe how the shape of a bell-shaped curve represents numerical data.
• Explain the method for calculating the range.
• Describe how standard deviation represents numerical data.
• Describe how standard deviation appears on the bell-shaped curve.
• Describe how standard deviation relates to probability.
• Describe how random sampling generates numerical data.

Class Vocabulary

Vocabulary TermDefinition
A common type of histogram characterized by a high center, tapered sides, and bell-flared edges. A bell-shaped curve reflects conditions that exhibit natural variation.
A collection of numbers or facts that is used as a basis for making conclusions.
A numerical expression representing a part of a larger whole. A fraction can be converted to a decimal by dividing the upper number, or numerator, by the lower number, or denominator.
A visual graph that shows the frequency of a range of variables.
The portion of a histogram that lists the range of variables.
The average of a numerical set. It is found by dividing the sum of a set of numbers by the number of members in the group.
The value of a numerical set that equally divides the number of values that are larger and smaller. For example, in a set containing nine numbers, the median would be the fifth number.
The value of a numerical set that appears with the greatest frequency.
Variation resulting from sources that are normal and expected. Natural variation is predictable over time.
A numerical expression that includes a percent sign, with 100 assumed as the denominator.
The mean of a numerical set that includes all the numbers within the entire group.
The likelihood that a particular event will happen in the future. Probability can be expressed as a fraction, ratio, or percentage.
A set of activities that uses resources to transform inputs into outputs. Essentially, a process describes the way "things get done."
The process of collecting and analyzing only a small representative portion of a larger group. Each item must have the same likelihood of being selected.
The difference between the smallest and the largest values within a numerical set.
A numerical expression representing a part of a larger whole or proportion. A ratio consists of two numbers separated by a colon.
A mean of a numerical set that includes an average of only a portion of the numbers within a group.
A number representing the degree of variation within a numerical set.
The science of collecting, summarizing, and analyzing numerical data. Statistics makes it possible to predict the likelihood of events.
Variation resulting from one or more sources that involve a fundamental change in a process. Unnatural variation is undesirable.
A difference between two or more similar things.
The portion of a histogram that indicates the frequency of each variable.