Introduction to Probability and Statistics for Engineers and Scientists
24 Chapter 2:Descriptive Statistics In other words, adding a constant to each data value does not change the sample variance; wh ...
2.3Summarizing Data Sets 25 Definition Thesample 100ppercentileis that data value such that 100ppercent of the data are less tha ...
26 Chapter 2:Descriptive Statistics TABLE 2.6 Population of 25 Largest U.S. Cities, 1994 Rank City Population 1 New York, NY.... ...
2.4Chebyshev’s Inequality 27 30 31.5 34 27 40 FIGURE 2.7 A box plot. SOLUTION A stem and leaf plot of the data is as follows: 6 ...
28 Chapter 2:Descriptive Statistics When the size of the data set is specified, Chebyshev’s inequality can be sharpened, as indi ...
2.4Chebyshev’s Inequality 29 TABLE 2.7 Top 10 Selling Cars for 1999 1999 Toyota Camry................. 448,162 Honda Accord.... ...
30 Chapter 2:Descriptive Statistics Proof Letyi=xi− ̄x,i=1,...,n. For anyb>0, we have that ∑n i= 1 (yi+b)^2 ≥ ∑ i:yi≥ks (yi+b ...
2.5Normal Data Sets 31 2.5Normal Data Sets Many of the large data sets observed in practice have histograms that are similar in ...
32 Chapter 2:Descriptive Statistics FIGURE 2.10 Histogram of a data set skewed to the left. FIGURE 2.11 Histogram of a data set ...
2.6Paired Data Sets and the Sample Correlation Coefficient 33 Approximately 99.7 percent of the observations lie within x ̄± 3 ...
34 Chapter 2:Descriptive Statistics FIGURE 2.12 Histogram of a bimodal data set. TABLE 2.8 Temperature and Defect Data Day Tempe ...
2.6Paired Data Sets and the Sample Correlation Coefficient 35 35 28 21 14 7 Number of defects 20 21 22 23 24 25 26 27 28 29 30 3 ...
36 Chapter 2:Descriptive Statistics be a negative value. Because the same statements are true about theydeviations, we can concl ...
2.6Paired Data Sets and the Sample Correlation Coefficient 37 Properties ofr − 1 ≤r≤ 1 If for constantsaandb, withb>0, yi=a ...
38 Chapter 2:Descriptive Statistics r = –.50 r = 0 r = –.90 FIGURE 2.14 Sample correlation coefficients. The sign ofrgives the d ...
2.6Paired Data Sets and the Sample Correlation Coefficient 39 85 80 75 70 65 60 55 Pulse rate 10 Years of school 12 14 16 18 20 ...
40 Chapter 2:Descriptive Statistics of exercise and good nutrition; or it may be that it is not knowledge that is making the dif ...
Problems 41 Problems.......................................................... The following is a sample of prices, rounded to ...
42 Chapter 2:Descriptive Statistics Means of Transportation to Work Average Travel Region, Division, Percent Using Public Time t ...
Problems 43 Means of Transportation to Work Average Travel Region, Division, Percent Using Public Time to Work^1 and State Trans ...
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