What's Up With the Weather?

Student Handout

Temperature Trends Part II

Procedure

In Part 1, you graphed your temperature data. If you want to see beyond the regular summer through winter temperature cycle, you must filter the data with a 12-Month Moving Average. A moving average allows you to do a continuous average of your data.

1. Retrieve your Temperature Graph. The next step is prone to errors so work carefully and check each other's work.

   1. Add all 12 temperatures of your year and circle the SUM. Divide that sum by 12 to find the first average.

   2. Plot this average by putting a green dot on the June line.

   3. To move the average ahead one month, subtract your January temperature from your circled sum of all 12 months, and add the January temperature from the next year.

   4. Divide your new sum by 12. This is your second average. You now have a new 12-month average. Plot this with a green dot on the July line.

   5. Now find your third moving average. Subtract your February temperature from your second average sum and add your February temperature from the next year. Divide your new sum by 12. This is your third average. Plot it with a green dot on the August line. See Moving Average Algorithm below for a model.

2. In the same manner, complete all 12 moving averages. You will find that you can plot only seven moving averages on your graph (June to December). Find the group with next year's data to plot your last five averages. Another group will plot the five moving averages (January to May) on your chart (except for group with the first year, 1989).

3. Connect your 12-month moving average points with a red line. Make a smoothly flowing line from point to point. The 12-month moving average line now shows the longer term changes in Boston temperatures without the confusing seasonal changes.

4. Tape the graphs together. What do you see?

Questions
Write your answers on a separate sheet of paper.

1. Were your original ideas about the temperature trends supported by the 12-month moving average?

2. Are long-term changes evident in the 12-month moving average trend?

3. What might you do to extend your view of long-term temperature change?

4. How does this help explain why there is so much controversy about long-term climate change?

5. The moving average is an example of a statistical analysis technique and can be used to filter any data containing known regular cycles. Where else might you use a moving average to reveal useful information?