After completing this activity, students should be able to:

1. Explain that more than one data value is needed to interpret results (30 year periods are used by the National Weather Service to establish "means").
2. Explain that a data set is meaningless unless it is interpreted.
3. Describe and calculate (either using a computer package or calculator) three possible statistics used to interpret a data set.

Prerequisite skills: Ability to use a computerized statistical package, or an understanding of statistical concepts, and the ability to calculate measures of central tendency and dispersion.

Time needed: 30 minutes to use a statistical package, or a class period to explain and understand each concept.

Introduction

One data value, such as the high temperature for the day, doesn't really mean very much because, we don't know whether that temperature is a typical (average) or, high or low value. Once we have a month's, or year's-worth (or more) of data, we can begin t o organize and describe it so that we can figure out what is typical or unusual. There are three common numerical ways that are often used to interpret a data set: Means and Extremes, Trends, and Variability.

1. Means and Extremes

A weather report describes daily weather in terms of means and extremes. Is it high, or maximum temperature, a record -- an extreme -- for the day, or is it just a typical (average or mean) value for the time of year?

Look at the temperature data on the attached Table (1). The values are the yearly-averaged highs and lows for a sample of available National Weather Service information. The daily high, or maximum, temperature was measured each day for a year, and average d to obtain a value for the yearly high temperature, In the same way the low, or minimum temperature was measured each day and averaged to obtain the yearly low. See the charts below for examples.

Find the extremes in the data set. Look for the highest of both the high and low average temperatures, and the lowest of both the high and low average temperatures. Record those temperatures, and the year or years in which they occurred, below.

A. Yearly highs
Highest Year/Years
_____ ________________________________
Lowest
_____ ________________________________

B. Yearly lows
Highest Year/Years
_____ ________________________________
Lowest
_____ ________________________________

C. Average/Mean High Temperature______________________

D. Average/Mean Low Temperature_______________________

E. Where______________, when______________, how_______

___________________________________________________

and by whom__________________is the official daily temperature taken in your area?

2. Trends

Scientists use many techniques to organize data. You may be familiar with several common kinds of graphs: bar, line or pie charts.

Construct a two-variable graph (temperature, time), or use a computer program to graph the yearly average high and low temperature data

A. Do you think that the temperatures are getting higher or lower over time? In other words, is a trend apparent?
___________________________________________________

Sometimes trends are apparent, but often they are not. To help detect trends, we can use a statistical technique to draw the best possible straight line through the data. The statistical technique used to draw the line or lines is called "regression", and the lines are called "regression lines". The lines provide the "best overall fit" to all of the data points in a sample. An upward or downward trend is easy to spot using this technique. Look at the graph for Olathe, Kansas, and examine the regression li ne.

B. Are trends apparent? If so, describe them._______________________
_____________________________________________________

A different statistical technique can tell us the strength of a relationship between two variables: it is called "correlation". Relationship strength is represented by a single number, the corrleation coefficient. The value of the number lies between 0 an d 1; the larger the number the stronger the degree of association between two variables. A positive number indicates that both variables are increasing over time, and a negative number indicates a decrease.

C. What does the correlation coefficient tell us about each of our data sets?

1. Average Maximum Temperatures________________________
_________________________________________________
2. Average Minimum Temperatures________________________
_________________________________________________
3. Variability

It is possible for two data sets to have the same average or mean, but very different variability. For example, two classes could have the same average score on a test, say 75, but most of the scores in one class might all fall between 70 and 80. A 90 in this class would really stand out. The scores in another class could be between 55 and 95 and still average 75. These scores are much more variable, and a 90 in this class would not seem so unusual.

A measure of variability called the "standard deviation" tells us how variable a data set is. If it is a small number then the data points are close together or are grouped, around the average score. If the standard deviation is large, then the data are s pread out, and are considered more variable.

Use a calculator or a computer software package to calculate the standard deviation of the yearly average highs and lows in your area.

Use the graph of the yearly average highs and lows for your area and the means you calculated in the first section above: draw a line indicating the mean for the highs and another line indicating the mean for the low values.

Next, draw lines one and two standard deviations about and below the mean (four lines in all). If the data are normally distributed (such data form a bell-shaped curve), then we would expect 68% of the data to fall within one standard deviation of the mea n and 95% of the data to fall within two standard deviations. Thus, if a yearly average temperature fell beyond two standard deviations, it would be expected only 2 1/2 % of the time and should seem unusual.

Look at graph with the lines drawn on it and determine which temperature values fall above and below one and two standard deviations, and record them below.

A. Yearly Highs

One standard deviation (1 S.D.)
_______________________________________________________________
Two standard deviation (2 S.D.)
_______________________________________________________________
B. Yearly Lows

One standard deviation (1 S.D.)
________________________________________________________________
Two standard deviation (2 S.D.)
________________________________________________________________
Reference

Hach - Quality Corner - #6123, #6125, Hach Company, P.O. Box 389, Loveland, CO 80539

What is your Carbon Contribution?

GLOBE Teacher's Key:

Students will be able to:

1. Explain the science concepts related to the mechanisms of the Greenhouse Effect and the carbon cycle.

2. State a hypothesis and gather data to test the hypothesis.

3. Construct a concept map using the concepts involved in this activity.

Prerequisite skills: Prerequisite skills and knowledge include skills in concept mapping, computation, skills knowledge of the mechanisms of the Greenhouse Effect and the carbon cycle, including sinks and sources of carbon dioxide.

Appropriate grade levels: High School, or upper Middle School levels. Prerequisite skills and knowledge could be sequenced to precede this activitiy, or taught at earlier grade levels.

Time needed: 2-4 classes over several weeks depending on the detail of data collected and analyzed.

Activity Background

Although carbon dioxide, methane, nitrous oxide, chlorofluoracarbons, and ozone collectively contribute to the greenhouse warming of the Earth, it is carbon dioxide that plays the largest (60%) single role in the warming process.

A variety of human activities, including deforestation, agriculture, the burning of fossil fuels, and cement production produce carbon dioxide. Of these activities, fossil fuel combustion accounts for about 85% of the carbon dioxide production per year. E nergy usage in industrialized countries has been chiefly responsible for the observed 25% increase in atmospheric carbon dioxide concentration over the past 100 years. Population increase in less industrialized countries over the next 100 years, coupled w ith increased energy requirements as these countries develop, are likely to shift a substantial part of human C02 production to other world regions.

As the number of humans and fossil fuel use increase, all of us must share the responsibility for possible global climate change produced by the additional carbon dioxide in the atmosphere, and work toward reducing the impact such change might bring.

1. Engagement

Based on student knowledge of the carbon cycle, review the major human activities which contribute or remove carbon dioxide from the carbon cycle.

Because an individual contribution of carbon dioxide is mainly through the use of energy, have students list all the ways they use energy during the day. Summarize this list on the black board; make the list as exhaustive and inclusive as possible. Classi fy each energy use as to the type of energy used; e.g., a clock-radio uses electricity. Finally, trace the electrical energy type "electricity" to its local source; e.g., coal-fired power plant.

2. Explore

In this activity, students will calculate the average per person production of C02 for the local area through the use of gasoline, generation of electricity and use of natural gas. If other energy sources are used in your area, list them and try to determ ine the C02 produced from using them.

Make the following calculations for a typical household in your area and record this information on the data sheet. Ask for a student/parent volunteer, use your own household, or use a class average to provide the data.

A. Direct Use

• 1. Transportation

• a. Cars - Find out how many miles the family car(s) were driven last year, and about how many miles per gallon of gas each car travels (the national average miles per gallon is 28 mpg). Divide the miles driven by the miles per gallon for each car. Each gallon of gas burned produces 20 pounds of C02 for cars and 21 pounds of C02 for trucks/vans.

• b. Airplanes - Find out how many miles family members flew last year. Flying 1 mile produces one-half pound of C02 per person.

• 2. Household Use - Determine what the fuel source is for electricity generation in your area by calling the power company. Obtain monthly bills for electricity and natural gas for a year or use a March or October bill and multiply times 12. Determine the kilowatt hours and therms used in a year, and then the pounds of C02 produced by each fuel source using the chart.

B. Indirect Use

Carbon dioxide is also released into the air when the products we buy are produced and transported. It is estimated that this indirect production of carbon dioxide is equal to the direct production. Multiple the total direct production of C02 by two to ge t the Total Indirect Pounds of C02 produced by a typical family in your area. (Divide this number by the number of individuals in the family to get Total Pounds of C02 Produced per Person in your area.)

C. Total Production

Add the direct and indirect production of C02 .

3. Explain

Be certain students understand how and why the calculations were made and that concepts such as KWH are defined/understood. Discuss the following questions:

1. Calculate the pounds of C02 saved if your car(s) averaged 5 more mile per gallon.

2. If one acre of trees can use 2.6 tons of carbon dioxide per year, how many acres of trees would be needed to absorb the C02 produced by the average person in your area?

3. Discuss ways to reduce the use of fossil fuel consumption/C02 release in each production category, (transportation, household and indirect use).

4. Try to determine the average direct C02 production per person in your country.

   ---

5. What are the indirect sources of C02 from:

7. a. Transportation (i.e., clearing vegetation to build roads, cement production to build roads)

9. b. Household use

Summarize the data collected by constructing a bar graph of the Total Direct C02 Produced (A3), C02 Produced from Transportation (A1), and C02 Produced by Household (A2).

Write a paragraph as a class or in small groups which describes the lifestyle of your community and its geographical features which might lead to the numbers you calculated. Share this information with the other Globe-Phase II Trace Gas experiment schools .

When you have received information from the other globe schools, compare and discuss the results. In small groups construct one hypothesis as to why the differences exist in the data between schools and decide on data which might be used to support or rej ect your hypothesis. Collect these data from the other schools and use it to evaluate your hypothesis. For example transportation differences may depend on type of cars driven, distance from school, driving age, use of cars, etc.

5. Evaluation

In small groups, have students construct concept maps using at least the following concepts: human activity, personal energy use, lifestyle, gasoline, KWH, industry, agriculture, deforestation, motor vehicles, electricity, global warming, carbon dioside, power plants. Place concepts on cards and have students arrange the cards on a sheet of paper with connecting words. Allow a few blank cards so students can add concepts if they wish.

References

Penn State - College of Education

http://www.ed.psu/dept/ci/sts/ toc.htms

Global Atmospheric Change - Investigation - Lesson 13

Environmental Science Activities by Dorothy B. Rosenthal, 1995, John Wiley and Sons, ISBN 0-471-07626-0

Global Warming - Social Studies Activities - High School, 1991, by Roberta Snow and Richard Golden, Climate Protection Institute, San Francisco, CA.