Activity 3.1

Temperature Patterns: Functions and Line Graphs

10 points

Due at the beginning of class, Wednesday, February 11, 2009

In this activity you will work with examples in which curves obtained by joining known points of the graph of a function can help you understand the data. These graphs are called line graphs. The temperature in a region varies over the year and is a function of the time of year. You will look at average temperature data as a function of month in various cities and investigate patterns in the data. You will also create a graph involving minimum wage data.

1. In problem #1, you will create several graphs. The graph you write on a separate sheet of paper does NOT need to be turned in. The graphs that you create in Excel SHOULD be copied and pasted into your Word document.

So, on a separate sheet of paper, which you do not need to turn in, sketch a curve that you think shows how the average temperature in Duluth, Minnesota (one of the coldest places in the continental U.S.), changes over the course of a year. (Think about when the temperature would be a maximum, when it would be a minimum, when it would be increasing, and so on.)

Next, you will follow the Excel directions below to create the line graph and bar chart. The data file you'll need is EA3.1.1 Avg Temp Four Cities.xls. Note that the directions below suggest a layout which does not include a title for the chart. Remember that in this class, we always give charts titles (and label their axes), so you should do it here too. (If you have a problem creating these graphs, try highlighting only through November to create the graph, and then click and drag the blue lines outlining your chosen data to include December).

2. How does the line graph for Duluth, Minnesota, compare with the one you created in #1?

3. Explain what the graphs you created show.

4. Which of the two types of graphs (line or column) do you think is preferable for these data, and why?

5. Use the line graphs you created previously to answer the following:
5. a. Identify, for each of the four cities when during the year the maximum average temperature occurs.

5. b. Identify, for each of the four cities when during the year the minimum average temperature occurs.

5. c. Identify, for each of the four cities when during the year the temperature is increasing.

5. d. Identify, for each of the four cities when during the year the temperature is decreasing.

5. e. Over the interval Jan - May, which city's temperature increased the fastest and how does the graph show that?

5. f. Identify where the graph of the average temperature of Duluth, Minnesota, is concave-upward and where it is concave-downward.

6. Retrieve the data file EA3.1.2 Min Wage.xls (or you could enter the data below, on minimum wage in years in which it increased, into an Excel worksheet).

6. a. Use Excel to create and label TWO graphs of these data: a scatterplot (make sure you select Scatterplot instead of Line in the Chart Wizard) with just the points shown, and a scatterplot using a line to connect the points (you may choose to show the points or not, and you may choose a smooth line or data points connected by line segments).

6. b. Which variable should be on the horizontal axis of these graphs and why?

6. c. Explain why your line graph (the one with the points connected) is not really appropriate for these data.

7. Retrieve the data set EA3.1.3 Normal Avg Temp.xls. Select ONE city from U.S. that appears in this file and create an appropriate graph of the data. (Source: National Oceanic & Atmospheric Association, www.noaa.gov/climate.html)

8. Interpret your graph and explain what the graph shows about the average temperature over the year in your city. (Your explanation should include a lot more detail that the title of the graph conveys and should include information about when, over the course of the year, the temperature is increasing, when it is a maximum, when it is concave-up, concave-down, and so on.)

Summary
In this activity, you compared bar graphs and line graphs, and used graphs to find maximum and minimum values of functions, intervals where the function is increasing, where it is decreasing, and where it is concave upward or concave downward. You learned how to use Excel to create line graphs and how to copy and paste data and insert rows in an Excel worksheet.