

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 CorePlus
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 zscore): 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 259265.)

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 297302.)

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 283293.)
