SCORE Mathematics

Standards Connections

A Devious Investigation:

A Lesson in Standard Deviation

by Debra Payne

with assistance from Judy Ebey, Shari Kaku, and Evelyn Schmitt

Introduction:

This investigation is designed have students develop an informal understanding of standard deviation by having students find the mean and standard deviation of their hometown and comparing them to a town with a similar mean but a different standard deviation.

Prior Knowledge:

Students should already know what the mean is and how to calculate it.

Grade Levels:

8 to college

Objective:

Students will internalize an informal understanding of standard deviation.

Resources:

Student Page (html) or Student Page (pdf)
This worksheet should be printed out for student use while they are doing this assignment.

Extension Page (html) or Extension Page (pdf): The an extension activity is designed either for students who have already had experience with standard deviation in previous courses (such as with IMP4 or CPM4), or for very students who need more of a challenge.

mean and standard deviation

U.S. Western Historical Climate Summaries

Mean Temperatures in the US.

Regional Climate Summaries

City Information

Process:

Supplies:

One copy of the Student Page per student

If you choose to do the extension, you also need the Extension Page.

Calculators that will calculate mean and standard deviation. It is designed to use a TI-83 or a TI-82, but you can modify the lesson use others.

Step One: Students will go to the Internet to find the average monthly temperature in either their city or a city closest to you. Then they go to the menu for General Climate Summary Tables for Temperature and Precipitation to find the following information. There are many choices on this page. Make sure students choose the tables with these titles.

Temperature Monthly Average Mean:

Temperature Mean for winter and summer

Precipitation Mean

Snowfall Mean

They will use a calculator to find the mean and the standard deviation for the Temperature Monthly Average Mean of this sample.

Step Two:
Students will use the data they gathered from the Internet to write a paragraph to describe the kind of weather, or climate, in your town.

Step Three:
Next they will go to the Internet and find a city in a different state that has a mean temperature that is with 1.0 degree from your city. This standard deviation must differ at least 2.0 degrees. If not, they must go back to the data table and find another city.

Step Four:
Students will compare the two standard deviations and make a conjecture to answer the question: What does it mean if two cities basically have the same mean temperature, but different standard deviations.

Step Five:
Next they find information to write a paragraph to describe the kind of weather, or climate, in this other town. They may want to consider

the temperatures in the winter and summer months

precipitation

snowfall

humidity

sunshine

wind data

Step Six:
Finally, they use gathered and the means and standard deviations of both cities to answer the question: What does it mean if two cities basically have the same mean temperature, but different standard deviations.

Learning Advice:

This symbol appears where students are required to write and make conjectures.

This symbol indicates that students use a TI-83 or TI-82 to do calculations.

This symbol means the students must log on the Internet.

You should do this investigation before giving it to your students. All of the regions at Regional Climate Summaries are set up independently and they vary drastically.

Full Class Access - an on-line computer lab at school
Have students work in pairs. Require that each pair use a different city. Due to time constraints, you may want them to do the writing involved in Steps 2, 4, 5 and 6 at home.

Limited Class Access - computers accessible at home, or a few at school
Have students work in pairs that they choose.

No Class Access - only teacher has access
The teacher can collect that data for the students. Students in pairs or groups can do the analysis.

Evaluation:

Step Six is the assignment assessment.

For the Extension, Step Nine is an assessment.

Extensions:

Require that each pair use a different city. Compile the information from the class. Have individuals compare two cities other than their own and write an essay using the statistics to explain which city they were prefer to move to and why.
Extension Page: The an extension activity is designed either for students who have already had experience with standard deviation in previous courses (such as with IMP4 or CPM4), or for very students who need more of a challenge.

Conclusion:

At the end of this investigation, students should have developed and internal understanding of standard deviation.

Feedback:

If you have suggests for how to make this activity run more smoothly, or you want to tell me what you liked about this activity, please email me.
If you have any comments or suggestions please email me at debpayne@earthlink.net

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California Academic Content Standards:

Grade 8-12:
Probability and Statistics
6.0 Students know the definitions of the mean, median, and mode of a distribution of data and can compute each in particular situations.
7.0 Students compute the variance and the standard deviation of a distribution of data.
Probability and Statistics- Advanced
10.0 Students know the definitions of the mean, median, and mode of distribution of data and can compute each of them in particular situations.
11.0 Students compute the variance and the standard deviation of a distribution of data.

NCTM Standards:

STANDARD 10: STATISTICS
In grades 9-12, the mathematics curriculum should include the continued study of data analysis and statistics so that all students can--

summarize data from real-world situations
understand and apply measures of central tendency, variability, and correlation