 Mathematical Content CPMP Classrooms Helping Your Student Helping with Homework Preparing for Tests Preparing for College Research Base Evidence of Success

# Course 3, Unit 4 - Samples and Variation

Overview
This unit provides students with experience in thinking about and working with the variation in measurements. Following the ideas of American W. Edwards Deming, considered by many to be the father of Japanese industry's use of quality control, statistical methods are used increasingly in American industry to improve the quality of products. Companies that are committed to the improvement of their products require that the methods be understood by everyone, from employees on the shop floor to those in the executive suite. Called quality control, statistical process control, quality improvement, and other names, the techniques used are highly mathematical. In this unit, students will study the mathematics behind these methods.

Key ideas covered in additional depth in this unit are: percentiles, expected value, probability distributions, standard deviation, normal distributions, rare events, statistical significance, the Multiplication Rule of Probability, and the Addition Rule of Probability.

Students who have completed Course 3 are exceptionally well prepared to take Advanced Placement (AP) Statistics. The AP Statistics syllabus includes all of the statistics and probability topics in Core-Plus Mathematics Courses 1, 2, and 3, except the control charts in Lesson 3 of this unit.

New Key Ideas from Course 3, Unit 4

• Standardized value (or z-score): The (positive or negative) number of standard deviations a given value lies from the mean in a distribution. (See page 243.)

• Binomial situations: A probabilistic situation with a fixed number of independent trials, each with two possible outcomes, and the same probability of success on each trial is called a binomial situation. The shape of a binomial distribution will be approximately normal if the expected number of successes is 10 or more and the expected number of failures is 10 or more. (See pages 259-265.)

• Central Limit Theorem: This theorem is a statement about the shape of the distribution of the means of all possible samples of a fixed size taken from a finite population. It says that the shape becomes more and more approximately normal as the sample size increases. (See pages 297-302.)

• Control chart (or run chart): A type of plot over time where observations from an industrial process are plotted in order of occurrence and checked for patterns that indicate that the process has gone out of control. (See pages 283-293.)