Abstract
This lesson is designed to develop students' critical thinking skills by introducing them to
misleading statistics. This lesson also introduces students to general
statistical terms and concepts.
Standards (NCTM)
Data Analysis
Formulate questions that can be addressed with data and collect, organize,
and display relevant data to answer them
- know the characteristics of well-designed studies, including the role of
randomization in surveys and experiments.
Select and use appropriate statistical methods to analyze data
- find, use, and interpret measures of center and spread, including mean and
interquartile range.
- discuss and understand the correspondence between data sets and their
graphical representations, especially histograms, stem-and-leaf plots,
box plots, and scatterplots.
Develop and evaluate inferences and predictions that are based on data
- use observations about differences between two or more samples to make
conjectures about the populations from which the samples were taken;
- use conjectures to formulate new questions and plan new studies to
answer them.
Student Prerequisites
- Educational:
Students should know:
- basic concept of average & data sets/collection.
- how data sets can be represented through different graphs.
- Technological:
Students must be able to:
- perform basic mouse manipulations such as point,
click and drag.
- use a browser such as Netscape for experimenting with
the activities.
Teacher Preparation
Teachers will need:
Students will need:
Lesson Outline
- Focus and Review
- Have students introduce themselves to the class by saying something
interesting about themselves.
- Explain the rules of name tag.
- Objectives
Students will learn their classmates' names and be introduced to misleading statistics.
- Guided Practice
- Monitor the students playing name tag outside, while recording each time a
student gets tagged.
- As a class use the
Bar Graph applet to create a bar graph portraying the number of times each
student got tagged.
- Teacher Input
- Describe a scenario where Billy Bob is trying to recruit the fastest runner
in the class.
- Tell the class that the recruiter is examining the graph you created in order to
determine the fastest runner.
- Discuss with the class why this graph does not necessarily display the data Billy Bob
needs to determine the fastest runner in the class and why this graph might be misleading.
- Independent Practice
- Have the students modify the graph without changing the data to try to convince
Billy Bob to recruit them.
Teacher Input
- Discuss a few of the students' graphs and what makes them misleading.
- Review what makes graphs misleading.
Guided Practice
- Go around the room and gather students' heights.
- Split students up into small groups.
- Have students graph the height data using the
Bar Graph applet and discuss
trends in the data.
- To be sure students are working, have each student record their observations.
Teacher Input
- Introduce/Review the terms sample, population, sample bias, and
stratified random sample.
- Discuss how these concepts relate to the tag and height data sets.
- Important question to ask - Does every name or thing in the whole group have
an equal chance to be in the sample?
Guided Practice
- Allow students working in pairs to explore the concepts of mean, median, and
mode by entering the height and tag data into the
Stem and Leaf applet.
- Students should record the shape or distribution of the data.
- Students can play with the data values and see how they effect the
mean, median, and mode values. Challenge students to create a data set
where the mean, median, and mode have strikingly different values.
Teacher Input
- Review the terms mean, median, and mode.
- Present the students with the following scenario
Martha the Math Professor has just given her statistics class a test to
evaluate how well they understand the material. When talking to another
professor, Martha is proud to report that her class had an average score of
81. However, during class the next day, half of the papers handed back say
"See Me". If the class average was 81, why does 50% of the class need
remediation?
- Let students enter the data set into the
Stem and Leaf applet.
- Discuss which value Martha uses for the 81 statement. What about the other
average values?
- Point out that an average can be the mean, median, or mode.
Independent Practice
- Split the class up into two groups.
- Hand out a copy of the Atlanta Braves Salaries for 1994 to each group.
- Group one must convince Group two to sign with the Atlanta Braves instead of
another team.
- Group two must convince Group one that they are underpaid and need a raise.
- Groups can only use the concept of average to make their claim.
Teacher Input
- Let students present their claims.
- Point out which average they used and
ask why?
- Define standard deviation and variance.
- Define normal, uniform, and skewed distributions.
- Discuss the signifiance of 68% of the observations fall within one standard
devation of the mean.
Guided Practice
- Hand out pennies to groups of, or individual, students.
- Students will flip their pennies 10 times and record the result each time.
- After 10 flips, allow students to explore the probability of flipping a heads
each time.
Teacher Input
- Record the probability results on the board.
- Theorical probability is 50/50, but the recorded probabilities aren't 50/50
why?
- Have students repeat the experiment with the Spinner Applet increasing the
number of trials.
- Record those results on the board, beside the other results.
- Sample size makes a difference in how close a person can get to the actual
distribution.
- With a large group, any difference produced by chance is likely to be small.
Independent Practice
- Hand out the newspapers and magizines.
- Students may look on the internet or through the papers for examples of
statistics.
- Define the term statistic and be sure to point out that everything covered in
class today was statistics.
- Closure
- Discuss a few of the statistics students found.
- Identify which statistics are misleading and how they are
misleading.
- Discuss how companies might use misleading statistics to convince consumers
to buy their products.
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