## Class Details

- Class Name:
- Statistics 231
- Difficulty:
- Intermediate
- Number of Lessons:
- 19

## Class Outline

- Statistics
- Variation
- Natural vs. Unnatural Variation
- Uses for Statistics
- Probability and Sampling
- Random Sampling
- Elements of Statistics Review
- Mean
- Types of Mean
- Median and Mode
- Mean, Median, and Mode Review
- The Histogram
- The Bell-Shaped Curve
- Types of Bell-Shaped Curves
- Range
- Standard Deviation
- Standard Deviation and the Bell-Shaped Curve
- Standard Deviation and Probability
- Bell-Shaped Curves and Standard Deviation Review

## Objectives

- Define statistics.
- Define variation.
- Differentiate between natural and unnatural variation.
- Describe how statistics relate to variation.
- Describe probability and its relationship to sample size.
- Define random sampling.
- Explain how to find the mean of a set of values.
- Distinguish between the two types of mean.
- Define median and mode.
- Describe a histogram and its uses.
- Explain the bell-shaped curve.
- Describe the types of bell-shaped curves.
- Define range.
- Define standard deviation.
- Describe the relationship between standard deviation and the bell-shaped curve.
- Describe the relationship between standard deviation and probability.

## Job Roles

## Glossary

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

average | Also known as the mean. The approximate value of each number in a set of numbers. The average is found by dividing the sum of a set of numbers by the number of members in the group. |

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. Data is collected by manufacturers about their facilities. |

fraction | A math expression with two numbers placed above and below a division line. A fraction indicates the number of divisions or portions and the size of each division or portion. |

Gaussian distribution | A common type of histogram characterized by a high center, tapered sides, and bell-flared edges. Gaussian distribution is another name for a bell-shaped curve. |

histogram | A visual graph that shows the frequency of a range of variables. Histograms are typically used to measure distribution patterns. |

horizontal scale | The portion of a histogram that lists the range of variables. The horizontal scale runs across the bottom of the histogram and is usually read from left to right. |

mean | Also known as the average. The approximate value of each number in a set of numbers. The average 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 within a numerical set that appears with the greatest frequency. The mode is the number that repeats the most within a set. |

natural variation | Variation resulting from random, normal differences that are expected and inevitable. Slight differences in raw materials are one cause of natural variation. |

normal distribution curve | A common type of histogram characterized by a high center, tapered sides, and bell-flared edges. Normal distribution curve is another name for a bell-shaped curve. |

percentage | An amount expressing what portion of a whole is present. Percentages are similar to fractions or decimals expressed in hundredths. |

population mean | The mean of a numerical set that includes all the numbers within the entire group. The population mean is helpful in making informed decisions based on an entire group. |

predictions | A forecast of coming events. Predictions allow manufacturers to make informed decisions about their facilities, parts, purchasing and other various areas. |

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

process | The series of activities that leads to a desired result. There are many processes in manufacturing, and they often lead to production of a part. |

random sampling | The process of collecting and analyzing only a small representative portion of a larger group. Random sampling dictates that each item must have the same likelihood of being selected. |

range | The difference between the smallest and the largest values within a numerical set. Range shows the amount of variation in a 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 | A representative part from a larger group. A larger sample increases accuracy. |

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

scrap | Any material not used to create the final part. During most machining operations, scrap appears in the form of chips. |

standard deviation | A number representing the degree of variation within a numerical set. Calculating the standard deviation of a numerical set shows the average amount of deviation. |

statistics | The science of collecting, summarizing, and analyzing numerical information, which is often used to make good decisions with confidence in an otherwise uncertain environment. |

tolerances | An unwanted but acceptable deviation from a given dimension. Checking for accurate part tolerance is done after a successful first part run. |

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

variation | Any difference that exists between two or more related things. |

variation | Any difference that exists between two or more related things. Variation is an unavoidable occurrence. |

vertical scale | The portion of a histogram that indicates the frequency of each variable. The vertical scale runs along the side of a histogram from bottom to top. |