#### Averages & Variation

Course:

Probability & Statistics-College Prep (Grade 12)

Unit Number:
2

Estimated Duration:
20 days

Unit Rationale:
This unit establishes standard statistics used throughout the course, building on the students' prior knowledge of averages. Real-world data sets and graphical representations of the data (including box-and-whisker plots) are incorporated throughout the unit. In addition to pencil and paper calculations, the calculator and computer are heavily utilized to analyze data sets numerically and graphically. Students are challenged to answer questions including "Why are descriptive statistics needed at all?" and "Why can't averages alone be used to describe data?" (Understanding Basic Statistics, 3e, Brase&Brase: Ch. 3.1, 3.2, 3.3)

Unit Goal:
SWBAT analyze data sets using measures of central tendency and measures of variation.

Prior Knowledge:
SWBAT apply arithmetic skills with sums, squares, and square roots.

Unit Assessment:
Analyze the Titanic dataset (taken from http://biostat.mc.vanderbilt.edu/twiki/bin/view/Main/DataSets) in order to determine whether or not the philosophy "women and children first" was actually followed when boarding the lifeboats.

Lesson Plans:

Lesson Number
Number of Days
Lesson Objective
Lesson Assessment
Benchmark or Standards
LP1 3Acquring & Integrating LPs
SWBAT analyze data sets using measures of central tendency (mean, median, mode).
Given dataset on length of commute to school, calculate mean, median, and mode and explain these computations; explain what it means for an average to be resistant; create 5-item dataset with mode 86, median 88, and mean 90.Indiana PS 1.1

LP2 3SWBAT analyze data sets using measures of variation (variance, standard deviation).Compare two datasets of test scores using measures of variation; construct a dataset with std dev 0.PS 1.1

LP34SWBAT analyze data sets using box & whisker plots.
Given dataset on LSU scores in 2005 and 2006 season, find 5 number summary; represent in box and whisker plot; and compare/contrast results; create 7-item dataset with Q1=80, median=88, max=100.PS 1.1, 1.2

1
10 multiple choice questions (without calculator); 1 short answer (with calculator); 1 error analysis calculating standard deviation (with calculator). PS 1.1
LP4 2Extending & Refining LPs
SWBAT analyze the effect of outliers on measures of central tendency and measures of variation.
Given datset on LSU scores, construct box and whisker plot with and without outliers; compute trimmed mean.PS 1.1, 1.2

LP5 2SWBAT analyze measures of central tendency and measures of variation using Minitab (or some other statistical software program).Generate descriptive statistics and boxplots for two datasets using Minitab and then explain these results; explain why using a computer is/is not helpful in statistical analysis.PS 1.1, 1.2

LP64Using Knowledge Meaningfully LP
SWBAT apply measures of central tendency and measures of variation to real-world data.
Analyze the Titanic dataset (taken from http://biostat.mc.vanderbilt.edu/twiki/bin/view/Main/DataSets) in order to determine whether or not the philosophy "women and children first" was actually followed when boarding the lifeboats.
PS 1.1, 1.2

1Performance Assessment
Part I: The family of a 14 year-old third class passenger, Miss Fortune, who died in the sinking of the Titanic decides to sue the Harland & Wolf ship-building company. The family claims that women and children were not given a fair chance to board the already-scarce lifeboats. Select the role of family member of Miss Fortune or representative from Harland & Wolf. Based on this role, make your case for or against the claim that the “women and children first” philosophy was followed onboard the Titanic.
Part II: analyze additional graphs/data from the Titanic dataset
PS 1.1, 1.2

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