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Math 011 – CHAPTER 3 Statistics for Describing, Exploring, and Comparing Data Measure of Center Mean Advantages Disadvantage Example: Median Example: Mode Example: Midrange Properties Example: Round Off Rules: Example: Find the mean, median, mode, and midrange for each of the following sets: Critical Thinking of Measures of Center Identify why the mean and median are NOT meaningful statistics a. Rank (by sales) of selected statistics textbooks: 1, 4, 5, 3, 2, 15 b. Numbers on the jerseys of the Cleveland Cavs when they won the 2016 NBA Champs: 23, 00, 5, 2, 8, 24, 52, 9 Class size: California’s mean is 20.9 students per teacher. Alaska’s mean is 16.8 students per teacher. What is the combined mean? Calculating the Mean from a Frequency Distribution Weighted Mean Example: For this Summer Statistics class, the instructor assigns the weight 0.20 to HW, 0.10 to Lab activities, 0.20 to Quizzes, 0.30 to Tests, and 0.20 to Final Exam. What is a student’s resulting grade if she got 95 on HW, 100 on Lab, 82 on Quizzes, 89 on Tests, and 93 on the Final Exam? Measure of Variation Range Standard Deviation Properties of Standard Deviation Example: Comparing Measures of Variation Range Rule of Thumb Example: a. Use the Range Rule of Thumb to find the minimum and maximum “usual” numbers of chocolate chips in Chips Ahoy using the table. b. Estimate s using the Range Rule of Thumb if the minimum chocolate chip is 19 and the maximum chocolate chip count is 30 for Chips Ahoy. Variance Properties Example: Example: IQ scores have a bell-shaped distribution with a mean of 100 and standard deviation of 15. What percentage of IQ scores are between 70 and 130? Between 85b and 115? Chebyshev’s Theorem Example: Coefficient of Variation Example: Find the coefficient of variation for each sample, and then compare the variation. Chips Ahoy cookies have a mean of 24.0 chips and standard deviation of 2.6 chips; Coke has a mean of 0.81682lb and standard deviation of .00751lb. Compare the number of chocolate chips to weights of Coke. Z score Example: The author of the text measured his pulse rate to be 48 beats per minute. Is that pulse rate unusual if the mean adult male pulse rate is 67.3 beats per minute with a standard deviation of 10.3? Percentiles Quartiles Other Statistics 5-Number Summary Boxplot Construction Example: Outliers Important Principles