# UTPA STEM/CBI Courses/Probability and Statistics/Statistics

Course Title: Contemporary Mathematics

Lecture Topic: Statistics

Instructor: Roger Knobel

Institution: The University of Texas - Pan American

## Backwards Design

Course Objectives

• Primary Objectives- By the end of this unit, students will be able to:
• Compute the mean and standard deviation of a data set.
• Use the mean and standard deviation to make inferences.
• Sub Objectives- The objectives will require that students be able to:
• Use a calculator to perform basic statistics computations.
• Difficulties- Students may have difficulty:
• Computing the mean of a data set given as a frequency table.
• Computing the standard deviation of a data set.
• Interpreting the meaning of standard deviation.
• Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
• Make sense of basic statistics used in news reports.

Model of Knowledge

• Concept Map
• Bar graphs
• Frequency tables
• Mean of a data set
• Standard deviation of a data set
• Content Priorities
• Enduring Understanding
• Understand the standard deviation as the spread of data values away from the mean of the data values.
• Be aware that knowing the mean of a data set can provide very limited information when making decisions.
• Important to Do and Know
• Be able to compute the mean of a data set summarized in a frequency table.
• Be able to compute the standard deviation of a data set summarized in a frequency table.
• Worth Being Familiar with
• Chebyshev's Inequality for general distributions
• Empirical Rule for normal distributions

Assessment of Learning

• Formative Assessment
• In Class (groups)
• Short in-class problem sets.
• Homework (individual)
• On-line quiz or homework problems
• Longer homework problems.
• Summative Assessment
• Questions on the unit and final exams.

## Legacy Cycle

OBJECTIVE

By this unit, students will be able to:

• Compute the mean, median, and mode of a data set.
• Compute the standard deviation of a data set.
• Use the mean, median, mode, and standard deviation to make inferences.

The objectives will require that students be able to:

• Use a calculator to perform basic statistics computations.

THE CHALLENGE

You are about to register for an important course required for your graduation. There are two sections of the course, one taught by Dr. Smith and the other by Dr. Jones. Both instructors are known to be very good; a friend of yours took the class from Dr. Jones last semester and tells you that at the end of the semester, the class average was 75%. You ask another friend who took Dr. Smith, who tells you that the class average was 80%. Which class will you register for, and why?

GENERATE IDEAS

Collect, compare, and contrast reasons for selecting each instructor.

MULTIPLE PERSPECTIVES

• Use a spreadsheet to show different data sets that have the same mean.
• Give examples from the news that reference only the mean.
• Class lecture on mean, median, mode, and standard deviation.

RESEARCH & REVISE

Ask students to construct possible data sets for each of the instructors in the Challenge Question, creating a scenario in which Dr. Jones might be preferred, and another scenario in which Dr. Smith is preferred.

GO PUBLIC

Unit or final exam question(s).

## Pre-Lesson Quiz

1. What is the mean of the data set {3, 6, 1, 1, 15, 4, 4}?
2. Create a frequency bar graph of the data set {3, 6, 1, 1, 15, 4, 4}
3. A data set consists of the value 10 with frequency 3, 12 with frequency 2, 5 with frequency 6, and 8 with frequency 1. Write out the data set as a list of numbers. What is the mean of this data set?

1. A recent study estimated the mean length of fish in Lake Willow to be 12" with a standard deviation 8", and the mean length of fish in Lake Sunshine to be 15" with a standard deviation of 3". From experience you've estimated that there are the same number of fish in both lakes, but you really hope to catch a record size fish. The two lakes are in opposite directions; which lake would you choose to fish, and why?
2. Construct a bar graph, mean, and standard deviation for each of the following data sets.
• {5, 8, 1, 3, 3, 6, 2, 5, 10, 5}
• {4, 6, 6, 3, 4, 3, 5, 6, 5, 5}