<p>MTH 243 Introduction to Probability and Statistics Summer 2012</p><p>Measures of Center (Section 2.1)</p><p>1. The following list gives the high temperatures in 36 US cities on July 20, 2012 (source: http://www.nws.noaa.gov/xml/tpex/scs.php).</p><p>CITY HI </p><p>ABILENE TX 93 AKRON CANTON 92 ALBANY NY 94 ALBUQUERQUE 100 ALLENTOWN 95 AMARILLO 92 ANCHORAGE 60 ASHEVILLE 86 ATLANTA 88 ATLANTIC CITY 95 AUSTIN 90 BALTIMORE 98 BATON ROUGE 89 BILLINGS 73 BIRMINGHAM 87 BISMARCK 72 BOISE 82 BOSTON 97 BRIDGEPORT 92 BROWNSVILLE 87 BUFFALO 85 BURLINGTON VT 95 CARIBOU 85 CASPER 72 CHARLESTON SC 86 CHARLESTON WV 94 CHARLOTTE 93 CHATTANOOGA 91 CHEYENNE 68 CHICAGO 95 CINCINNATI 90 CLEVELAND 91 COLORADO SPGS 77 COLUMBIA SC 91 COLUMBUS GA 89 COLUMBUS OH 93</p><p> a. Find the mean of the data:</p><p> b. Find the median of the data:</p><p> c. Find the mode of the data:</p><p> d. Throw out the lowest value and recalculate the mean, median and mode using only the remaining 35 values. MTH 243 Introduction to Probability and Statistics Summer 2012</p><p> d.i. New mean:</p><p> d.ii. New median:</p><p> d.iii. New mode:</p><p> e. Discuss how the mean, median, and mode are affected by extreme values (high or low). Construct another (small – about 5 data points) set of data to illustrate your ideas.</p><p>2. Construct a data set where the mean = median = mode.</p><p>3. Construct a data set where the mean > median.</p><p>4. Make a general statement about a characteristic of the data you might if the mean > median. MTH 243 Introduction to Probability and Statistics Summer 2012</p><p>5. Most parents brag that their child is “above average”. Is it possible for say, 80% of a data set to be above the average (mean)? Construct a data set where this is so.</p><p>6. Do problem 7 on page 16 of your book.</p><p>7. Which measure of center (mean, median, or mode) would best describe the following sets of data? Give justifications for your answers.</p><p> a. The typical size of shoe sold in a store. ______</p><p> b. The typical weights of football players on a team. ______</p><p> c. The typical cost of homes in a community. ______</p><p> d. The typical age of 7 people in a family if six of them are under 40 and one is 96 years old.______</p><p> e. The typical price of a textbook in a bookstore.______</p><p>8. Recall that µ is the symbol representing the population mean (parameter) and (xbar) is the sample mean (statistic). For each of the following write µ or next to it to indicate if it most likely represents a population or sample mean, respectively. MTH 243 Introduction to Probability and Statistics Summer 2012</p><p> a. The average number of letters per word in the Gettysburg Address by Abraham Lincoln is 4.29. _____</p><p> b. The average number of red skittles in a pack of Skittles is 4.56. _____</p><p> c. The average number of 8-oz cups of coffee Americans drink per day is 3.1. _____</p><p> d. The average number of red skittles in my 4 packages of Skittles is 3.5. _____</p><p>9. Find the mean, median and mode of the following data set:</p>