Copyright © 2011 Pearson Education, Inc. Putting Statistics to Work Discussion Paragraph 6A(write at least 5 sentences) 1 web Salary Data New York Marathon Tax Statistics Education Statistics 1 world Averages in the News Daily Averages Distributions in the News

Copyright © 2011 Pearson Education, Inc. Slide 6-3 Unit 6B Measures of Variation

6-B Copyright © 2011 Pearson Education, Inc. Slide 6-4 Why Variation Matters Consider the following waiting times for 11 customers at 2 banks. Big Bank (three lines): Best Bank (one line): Which bank is likely to have more unhappy customers? → Big Bank, due to more surprise long waits

6-B Copyright © 2011 Pearson Education, Inc. Slide 6-5 Range The range of a data set is the difference between its highest and lowest data values. range = highest value (max) – lowest value (min)

6-B Misleading Range CN (1) Consider the following two sets of quiz scores for nine students. Quiz 1: Quiz 2: Which set has the greater range? Would you also say that the scores in this set are more varied? Copyright © 2011 Pearson Education, Inc. Slide 6-6

6-B Copyright © 2011 Pearson Education, Inc. Slide 6-7 Quartiles The lower quartile (or first quartile) divides the lowest fourth of a data set from the upper three- fourths. It is the median of the data values in the lower half of a data set. The middle quartile (or second quartile) is the overall median. The upper quartile (or third quartile) divides the lower three-fourths of a data set from the upper fourth. It is the median of the data values in the upper half of a data set.

6-B Copyright © 2011 Pearson Education, Inc. Slide 6-8 The five-number summary for a data set consists of the following five numbers: low value lower quartile median upper quartile high value A boxplot shows the five-number summary visually, with a rectangular box enclosing the lower and upper quartiles, a line marking the median, and whiskers extending to the low and high values. The Five-Number Summary

6-B Copyright © 2011 Pearson Education, Inc. Slide 6-9 Best BankBig Bank low value (min) = 4.1 lower quartile = 5.6 median = 7.2 upper quartile = 8.5 high value (max) = 11.0 low value (min) = 6.6 lower quartile = 6.7 median = 7.2 upper quartile = 7.7 high value (max) = 7.8 Five-number summary of the waiting times at each bank: The corresponding boxplot: The Five-Number Summary

6-B Race Times CN (2a-b) Consider the following two sets of twenty 100- meter running times (in seconds): Set 1: Set 2: Compare the variation in the two data sets with a)five-number summaries and b)box plots. Copyright © 2011 Pearson Education, Inc. Slide 6-10

6-B Copyright © 2011 Pearson Education, Inc. Slide 6-11 Standard Deviation The standard deviation is the single number most commonly used to describe variation.

6-B Copyright © 2011 Pearson Education, Inc. Slide 6-12 The standard deviation is calculated by completing the following steps: 1.Compute the mean of the data set. Then find the deviation from the mean for every data value. deviation from the mean = data value – mean 2.Find the squares of all the deviations from the mean. 3.Add all the squares of the deviations from the mean. 4.Divide this sum by the total number of data values minus 1. 5.The standard deviation is the square root of this quotient. Calculating the Standard Deviation

6-B Copyright © 2011 Pearson Education, Inc. Slide 6-13 Standard Deviation Let A = {2, 8, 9, 12, 19} with a mean of 10. Find the sample standard deviation of the data set A.

6-B Calculating Standard Deviation CN (3a-b) 3. Calculate the standard deviations for the waiting times at a)Big Bank and b)Best Bank. BigB sum BestB sum 1.98 Copyright © 2011 Pearson Education, Inc. Slide 6-14

6-B Copyright © 2011 Pearson Education, Inc. Slide 6-15 The Range Rule of Thumb The standard deviation is approximately related to the range of a data set by the range rule of thumb: If we know the standard deviation for a data set, we estimate the low and high values as follows:

6-B Using the Range Rule of Thumb CN (4a-b) 4. Use the range rule of thumb to estimate the standard deviations for the waiting times at a)Big Bank and b)Best Bank. *hint, find range of times BigB BestB Compare the estimates to the actual standard deviation you found in the last problem Copyright © 2011 Pearson Education, Inc. Slide 6-16

6-B Estimating a Range CN (5a-b) Studies of the gas mileage of a Prius under varying driving conditions show that it gets a mean of 45 miles per gallon with a standard deviation of 4 miles per gallon. 5. Estimate the a)minimum and b)maximum gas mileage that you can expect under ordinary driving conditions. Copyright © 2011 Pearson Education, Inc. Slide 6-17

6-B Quick Quiz CN (6) Answer the 10 multiple choice questions of the quick quiz on p.388. Copyright © 2011 Pearson Education, Inc. Slide 6-18

6-B 6B Homework Discussion Paragraph 6A p.389: web 26. Web Data Sets 1 world 27. Ranges in the News 28. Summarizing a News Data Set 29. Range Rule in the News Class Notes 1-6 Copyright © 2011 Pearson Education, Inc. Slide 6-19