### Course 3 Unit 5 - Patterns in Variation 1st Edition

Patterns in Variation is the sixth major unit from the statistics and probability strand of the Contemporary Mathematics in Context program. Measures of variation for single-variable data introduced in Course 1, Unit 1, were the range, interquartile range, mean absolute deviation, and percentiles. Box plots were introduced to help visualize variation within a distribution. In Course 3, Unit 2, Modeling Public Opinion, sampling distributions were summarized with 90% box plots. (See the descriptions of Course 3 Units.)

#### Unit Overview

Patterns in Variation extends student understanding of the measurement of variation, develops student ability to use the normal distribution as a model of variation, and introduces students to the probability and statistical inference involved in the control charts used in industry for statistical process control.

 Unit Objectives To understand the standard deviation as a measure of variability in a distribution To understand the normal distribution as a model of variability To understand and be able to use the number of standard deviations from the mean as a measure of the position of a value in a normal distribution To understand the construction, interpretation, and theory of control charts To understand and apply the Addition Rule for mutually exclusive events

#### Sample Overview

The sample material is from Lesson 2 of this unit. Students are introduced to the normal distribution and its characteristics (symmetry and the relationship between the mean and the median). Students learned to measure variation using the standard deviation in Lesson 1 and now in Lesson 2 learn to interpret the number of standard deviations from the mean as a measure of location.

#### Instructional Design

Throughout the curriculum, interesting problem contexts serve as the foundation for instruction. As lessons unfold around these problem situations, classroom instruction tends to follow a common pattern as elaborated under Instructional Design.

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#### How the Statistics and Probability Strand Continues

In Course 4, students extend their understanding of the binomial distribution and how the binomial distribution is used in statistical inference to test a single proportion and to compare two treatments in an experiment.

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