AP Statistics Summer Assignment

Transcription

1 AP Statistics Summer Assignment Welcome to AP Statistics. You will need to able to use your graphing calculator with its statistics package to enter data, calculate simple statistics such as mean, median, or linear regression equation, and produce a box plot, scatter plot and histogram BEFORE the first day of class. Consult your manual if you are not already familiar with how to use your calculator. If you have any questions regarding this please the instructor. This is a mandatory assignment which is due at the beginning of the first class in August. If you have not yet purchased a graphing calculator, my recommendation is the purchase the TI-84 or TI-84 Plus. Consult your calculator manual for instructions on the keystrokes necessary to do the following operations: 1. See the data of 1994 Baseball Salaries towards the end of this assignment. Enter the salaries for the California Angels into List 1 and the salaries for the Baltimore Orioles into List 2. Do 1-Var Stats for each list and fill in the following table. Team Angels Orioles Mean Standard Deviation Min Q1 Median Q3 Max Know these terms (statistics): The mean, median and mode provide information about the number in the middle of a data set. The mean is the same as the average. The median is the middle number in the data set. The mode is the number that occurs most frequently. The range and standard deviation show how far data points spread out from the middle of the data set. The range is simply the highest number minus the lowest number. The standard deviation is a measure of how far data points are spread out from the mean of the data set. The larger the range and standard deviation are, the more the data points are spread out. Q1 is the first quartile or the 25th percentile, 25% of the data is below this value and 75% is above the value. Q3 is the third quartile or the 75th percentile, 75% of the data is below this value and 25% is above the value. 50% of the data is between Q3-Q1, which is the IQR (Interquartile Range). (a) Which team had the highest salary? (b) Which teach had the highest average salary? (c) Find each team s mode(s): Angels: Orioles: (d) What is the salary earned most frequently by an Angels player? (e) Make a boxplot of the Angels salaries and of the Orioles salaries on the same graph using your calculator. In the calculator, choose the boxplot that shows outliers. Sketch the boxplots below. Include a scale. (Hint: Zoom 9 on TI 83/84) Angels Orioles 1994 Baseball Salaries

2 (f) Outliers are individual observations that fall well outside the overall pattern of the data. Specifically, outliers are at least 1.5 x IQR above the third quartile or below the first quartile. To verify outliers in data, first find the IQR by Q3 Q1. Multiply IQR by 1.5. Subtract that value from Q1. Any salaries below that value are outliers. Add 1.5 x IQR to Q3. Any salaries above this are outliers. Verify $5,400,000 is an outlier in the 1994 Orioles Baseball Salaries. (g) Now, suppose that the Angels traded for three superstars, each making over $3,000,000/yr. These superstars replace the players with the lowest salaries on the team. Recalculate the mean, median and mode. Team Mean Median Mode Angels Compare the new statistics with the original ones. What statistic changed the most? the least? 2. In the space to the right, explain the humor in the cartoon below.

3 3. A scatterplot is a good way to investigate an association between two quantitative (numerical) variables. A point on the graph represents the combination of measurements for an individual observation. The following table shows sex, height (inches), and mid-parent height (inches) for a sample of 18 college students. The variable mid-parent height is the average of mother s height and father s height. Sex Height Mid-Parent Height M F F M F F M F F M F M M M F F M F (a) In the relationship between height and mid-parent height, which variable is the response variable (y) and which is the explanatory variable (x)? (b) Use your calculator to draw a scatterplot of the data for the y and x variables defined in part (a). Draw the scatterplot in the space below using different symbols for males and females. Label & scale your axes. (c) Does the association between height and mid-parent height appear to be linear? What are the differences between the males and females? (d) In TI 83/84 Calc: 2nd 0 Diagnostic On Enter. Find the regression line (y = a + bx) for the data points using LinReg (a + bx) in your calculator: STAT CALC #8. Record r for future use. (e) A histogram gives the number of data points that fall into equal intervals. Care must be taken in choosing the intervals because it can affect the shape of the graph and misrepresent the true data. A histogram is more convenient than a dot-plot or a stem and leaf plot because you don't have to represent each data point. However, you don't get to see the value of each data point. Use your calculator to draw a histogram of the height data. The y-axis represents frequency. Height

4 4. A stemplot (also called a stem-and-leaf plot) offers a quick way to picture the shape of a distribution while including the actual numerical values in the graph. Stemplots work best for small numbers of observations that are all greater than 0. List the stems vertically in increasing order from top to bottom, draw a vertical line to the right of the stems, and add the leaves to the right of the line. Arrange the leaves in increasing order from left to right. The Old Farmer s Almanac gives the growing season for major U.S. cities as reported by the National Climatic Center. The growing season is defined as the average number of days between the last frost in the spring and the first frost in the fall. The values are: (a) Make a stemplot by hand for these data. (Calculators can t create stemplots, but if you use the calculator to sort the data, it will be easier to make the stemplot). Are there any unusual values? Let 27 9 = 279 (b) The values for Los Angeles, San Diego, San Francisco, and Miami are represented by an asterisk (*) in the almanac rather than a number. There is a footnote explaining why. Given the above definition of growing season, why do you think there were difficulties with measuring this variable for these cities?

5 5. Collect one newspaper or magazine article that includes statistical concepts. *Be sure to include a copy of the article appropriately mounted with its source. This may include things like graphs, charts, or averages. It may also report conclusions made as a result of looking at this data. For the article, highlight the statistics mentioned and answer the following questions: (a) What was the purpose of the article? (b) Were any conclusions stated? If so, what were they? (c) Is the article convincing? That is, do you believe the stated results? Explain Baseball Salaries ANGELS ORIOLES Player Position Salary ($) Player Position Salary ($) C. Finley P 3,875,000 R. Palmerio 1b 5,406,603 M. Langston P 3,550,000 C. Ripkin Ss 5,400,000 C. Davis Of 2,400,000 M. Devereaux Of 3,375,000 J. Magrane P 1,500,000 S. Fernandez P 3,333,333 S. Owen Ss 1,250,000 B. Anderson Of 3,083,333 B. Jackson Of 1,000,000 B. McDonald P 2,675,000 J.Grahe P 925,000 C. Sabo 3b 2,000,000 D. Smith Of 700,000 C. Hoiles C 2,000,000 G. Myers C 700,000 H. Baines Of 1,800,000 C. Curtis Of 600,000 L. Smith P 1,600,000 T. Saimon Of 600,000 M. Mclemore 2b 1,000,000 G. DiSarcina Ss 400,000 M. Mussina P 750,000 J. Dopson P 400,000 L. Smith Of 750,000 C. Leflerts P 400,000 J. Moyer P 725,000 B. Panerson P 400,000 T. Hulett Lf 550,000 M. Leiter P 300,000 M. Eichhorn P 525,000 R. Hudler Lf 275,000 L. Gomez Lf 500,000 H. Reynolds 2b 230,000 A. Mills P 500,000 B. Sampan P 225,000 M. P 350,000 Wilhamson D. Easley Ss 170,000 J. Poole P 270,000 S. Lewis P 155,000 A. Rhodes P 230,000 M. Butcher P 150,000 J. Tackett C 162,500 E. Perez 1b 135,000 J. Hammonds Of 150,000 C. Turner Pc 125,000 J. Voight Of 150,000 J. Edmonds Of 117,500 D. Buford Of 130,000 P. Leftwich P 109,000 B. Pennington P 130,000 P. Carey Lf/of 115,000 M. Alexander Ss 109,000

6 2 6. Given y 12 x 3 (a) sketch the graph Algebra Practice (b) state the slope and y-intercept 7. Solve for x: SHOW ALL WORK x 6.1 (a) 82 3 (b) x (c) ln x (d) log x A line contains the point (2, 7). Write its equation in slope-intercept form if: (a) slope = ½ (b) another point on the line is (0, 2) Feel free to me at David_I_Beck@mcpsmd.org if you are having difficulty with the use of your calculator to answer these questions. On the first day of class, bring this work, one (1) 1.69 oz. bag of M&M s candy, your graphing calculator, a three-ring binder, notebook paper, and something with which to write. Have a great summer I m looking forward to meeting you in the fall!