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## CLASS DETAILS

## 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

## 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.

## Job Roles

## Certifications

SME- CMfgT

- CNC Lathe Operations
- CNC Milling Operations

- MSSC Quality Practices and Measurement

## Glossary

Vocabulary Term | Definition |
---|---|

bell-shaped curve | 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. |

data | A collection of numbers or facts that is used as a basis for making conclusions. |

fraction | 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. |

histogram | A visual graph that shows the frequency of a range of variables. |

horizontal scale | The portion of a histogram that lists the range of variables. |

mean | 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. |

median | 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. |

mode | The value of a numerical set that appears with the greatest frequency. |

natural variation | Variation resulting from sources that are normal and expected. Natural variation is predictable over time. |

percentage | A numerical expression that includes a percent sign, with 100 assumed as the denominator. |

population mean | The mean of a numerical set that includes all the numbers within the entire group. |

probability | The likelihood that a particular event will happen in the future. Probability can be expressed as a fraction, ratio, or percentage. |

process | A set of activities that uses resources to transform inputs into outputs. Essentially, a process describes the way "things get done." |

random sampling | 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. |

range | The difference between the smallest and the largest values within a numerical set. |

ratio | A numerical expression representing a part of a larger whole or proportion. A ratio consists of two numbers separated by a colon. |

sample mean | A mean of a numerical set that includes an average of only a portion of the numbers within a group. |

standard deviation | A number representing the degree of variation within a numerical set. |

statistics | The science of collecting, summarizing, and analyzing numerical data. Statistics makes it possible to predict the likelihood of events. |

unnatural variation | Variation resulting from one or more sources that involve a fundamental change in a process. Unnatural variation is undesirable. |

variation | A difference between two or more similar things. |

vertical scale | The portion of a histogram that indicates the frequency of each variable. |