2017AP Statistics Summer Packet.pdf

# The variance 2 s of a set of observations in the

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The variance 2 s of a set of observations in the standard deviation squared, meaning the average of the squares of the deviation of the observations from their mean.

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13 Example: Below is a list of test scores earned by AP Statistics students on the chapter 1 test. Find the mean and standard deviation. 88 72 96 68 81 1. Find the sample mean: 8 8 7 2 9 6 6 8 8 1 8 1 5 x 2. i x i x x 2 i x x 88 88 81 = 7 (7) 2 = 49 72 72 81 = -9 (-9) 2 = 81 96 96 81 = 15 (15) 2 = 225 68 68 81 = -13 (-13) 2 = 169 81 81 81 = 0 (0) 2 = 0 1. 2 i x x = 49 + 81 + 225 + 169 + 0 = 524 2. 2 5 2 4 5 2 4 1 3 1 1 5 1 4 i x x n . This is the variance! 3. 2 131 11.45 1 i x x n . This is the standard deviation.
14 Example Problem: TI 83/84 Calculator Instructions: Your calculator will compute the mean, standard deviation, and five number summary for you. 1. Press the STAT button on your calculator. #1 will be highlighted. Press ENTER. 2. Enter the data into L 1 . 3. Press 2 nd MODE (Quit) to exit the screen. 4. Press STAT, then move the cursor to the right so CALC is highlighted. #1 should be selected. Press ENTER. 5. The screen of your calculator will say 1-Var Stats. Type in L 1 (since your data is in List 1) ENTER. 6. The sample mean, x , is the first value given. Sx is the sample standard deviation. Scroll down to find the five number summary. Now, complete Worksheet C (Center, Spread, and 5-Number Summary); page 31

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15 Part 5: Quantitative Graphs While Bar Graphs and Pie Charts are used to graph Categorical Data , there are many methods of graphing Quantitative Data . These include dotplots, stemplots, histograms, and boxplots. DotPlots are one of the simplest statistical plots, and are suitable to small and moderate-sized data sets. DotPlots have the advantage of retaining the original data values (you could re-create the detailed, original data using the dotplot). Constructing a dotplot: 1. Draw a horizontal line, and label it with the variable being graphed (in the graph below, “Weight in ounces”). Provide a descriptive title, and label the axis with relevant data values. 2. Scale the axis based on the values of the variable. 3. Mark a dot above the number on the horizontal axis corresponding to each data value. Each dot represents a single observation from the set of data. Practice Problem: 1. In the Super Bowl, by how many points does the winning team outscore the losers? Here are the winning margins for the first 42 Super Bowl games: 25 19 9 16 3 21 7 17 4 12 17 5 10 29 22 36 19 32 4 45 1 13 35 17 23 10 14 7 15 7 27 3 27 3 11 12 3 3 10 18 17 4 Create a well labeled dotplot for the data above.