  Shop Essentials (Applied Mathematics)

# Statistics 231

Statistics provides a good overview of the various terms and methods commonly used for statistical analysis. In modern manufacturing, statistics are used as part of continuous improvement methods to analyze the data gathered during inspections to determine the quality of a product and examine the processes used to make it.

Every person in a manufacturing environment should have an awareness of what statistical terminology and be able to use statistical concepts in the workplace. After taking this class, a user will be able to calculate the mean, median, and mode for a set of data. The user will also be able to explain the difference between natural and unnatural variation, the use histograms and bell curves, and the meaning of standard deviation.

• Difficulty Intermediate

• Format Online

• Number of Lessons 19

• Language English TO GET STARTED SPEAK WITH A SPECIALIST AT 1.866.706.8665

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• 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. 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.