Temperature Patterns: Functions and Line Graphs

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1 activity 3.1 Temperature Patterns: Functions and Line Graphs 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 dat 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 dat You will also create a graph involving minimum wage dat 1. On the following axes, sketch a curve that you think shows how the average temperature in Fairbanks, Alaska, 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.)

2 Activity 3.1: Temperature Patterns Jan Feb Mar April May June July Aug Sept Oct Nov Dec Next you ll see how your graph compares to the actual data, and how the average temperatures over the year for four cities in different parts of the world compare. Instructions to Use Excel to Create Line Graphs d. Retrieve the Excel file EA3.1.1 Avg Temp Four Cities.xls from the CD or website. (Source: World Climate, Highlight the block of data for the months Jan through Dec, including the column and row headings but not the Year column (column N), and go to the Insert ta Select Line from the Charts group and select the first entry for Chart sub-type. With the graph still selected, from the Chart Layouts group, select Layout 7 and insert appropriate titles for your graph. Note that if you point (between vertical grid lines) on the unselected graph to one of the functions, the data values are given. Create a second graph using the same block of data, but this time use Column as the Chart type.

3 422 Excel Activities 2. How does the line graph for Fairbanks, Alaska, 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: Identify for each of the four cities when during the year the maximum average temperature occurs. Identify for each of the four cities when during the year the minimum average temperature occurs. Identify for each of the four cities when during the year the temperature is increasing.

4 Activity 3.1: Temperature Patterns 423 d. Identify for each of the four cities when during the year the temperature is decreasing. e. Over the interval Jan May, which city s temperature increased the fastest and how does the graph show that? f. Identify where the graph of the average temperature of Fairbanks, Alaska, is concave upward and where it is concave downward. 6. Retrieve the data set EA3.1.2 Min Wage.xls from the CD or website, or enter the following data on minimum wage in years in which it increased into an Excel worksheet. Year Wage($) Use Excel to create and label two graphs of these data: a scatterplot (make sure you select Scatterplot instead of Line in the Charts group) 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).

5 424 Excel Activities Which variable should be on the horizontal axis of these graphs and why? Explain why your line graph (the one with points connected) is not really appropriate for these dat 7. Retrieve the data set EA3.1.3 Normal Avg Temp.xls from the CD or website. Select three cities in different regions of the U.S. that appear in this file and create an appropriate graph of the dat (Source: National Oceanic & Atmospheric Association, Instructions to Use Excel to Copy and Paste Data For one of your cities, highlight the row of data for the city, go to the Clipboard group and click on the Copy icon. (It looks like two overlapping sheets of paper.) Or, you can press Ctrl and the letter C to copy. Then go to a new worksheet and select a new row from that sheet (leave the top row for labels, as shown in the Excel file EA3.1.3 Normal Avg Temp.xls. Click on Paste in the Clipboard group (or press Ctrl and the letter V.) Repeat with your other chosen cities. If you already have data in the first row, you can insert a blank row as follows: click on any cell in the first row. Then select Insert from the Cells group and then Insert Sheet Rows. When you have finished copying the data from your three cities, you should have the data and labels, similar to those in the first file used, in your new worksheet.

6 Activity 3.1: Temperature Patterns Interpret your graph and explain what the graph shows about the average temperature over the year in your three cities. (Your explanation should include a lot more detail than 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, 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.

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