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Unformatted text preview: 1 Chapter 2: Methods for Describing Sets of Data (Page 1998) Homework:14ab, 36, 43, 45, 51, 56, 64abc, 71, 79, 85, 89, 96 2 Section 2.1: Numerical Measures of Central Tendency (center): • Why we are interested in the central tendency of a set of measurements? The central tendency of a set of measurements is the tendency of the data to cluster (or center) about certain numerical values. Since it is very important to both descriptive and inferential statistics, there are many numerical measures such as mean , median , and mode available to estimate the central tendency of a set of measurements. One can not say which one is the best measure for the central tendency of a set of data because data have very different characteristic. 3 The most popular measure for the central tendency is the mean (or the arithmetic mean). We use the Greek letter µ to stand for the population mean and use the to stand for the sample mean. The mode is a useful numerical measure of the central tendency if one wants to know the measurement that occurs most frequently in the data set. The median is a good measure for the central tendency if there are several extremely large (or extremely small) measurements in the data. • Which one is the best numerical measure for the central tendency of a set of data? x 4 • Example 2.1 (Basic): The following data give the weekly expenditures (in dollars) on nonalcoholic beverages for 45 households randomly selected from the 1996 Diary Survey. 6.5 9.0 9.2 7.2 4.6 9.0 10.5 2.4 10.9 10.4 5.4 12.7 5.4 0.9 7.1 1.4 12.3 8.2 4.7 1.3 2.5 13.5 10.1 15.9 5.6 15.1 0.7 10.1 10.3 2.2 7.1 4.6 8.0 0.9 3.3 3.1 2.2 10.6 1.3 2.7 16.5 9.8 4.9 1.6 12.7 Use part of the SAS output in next 3 tables to find the sample size, mean, median, and mode for weekly expenditures. 5 Resul t s f or Exampl e 2. 1 Var i abl e=EXPENSE Moment s N 45 Sum Wgt s 45 Mean 6. 986667 Sum 314. 4 St d Dev 4. 468811 Var i ance 19. 97027 Skewness 0. 31744 Kur t osi s  0. 88551 USS 3075. 3 CSS 878. 692 CV 63. 96199 St d Mean 0. 666171 T: Mean=0 10. 4878 Pr > T 0. 0001 Num ^ = 0 45 Num > 0 45 M( Si gn) 22. 5 Pr >= M 0. 0001 Si gn Rank 517. 5 Pr >= S 0. 0001 6 Quant i l es( Def =5) 100% Max 16. 5 99% 16. 5 75% Q3 10. 3 95% 15. 1 50% Med 7. 1 90% 12. 7 25% Q1 2. 7 10% 1. 3 Range 15. 8 Q3 Q1 7. 6 Mode 0. 9 7 Ext r emes Lowest Obs Hi ghest Obs 0. 7( 27) 12. 7( 45) 0. 9( 34) 13. 5( 22) 0. 9( 14) 15. 1( 26) 1. 3( 39) 15. 9( 24) 1. 3( 20) 16. 5( 41) 8 Example 2.2 (Intermediate): Michelson conducted an experiment to determine the velocity of the light between 1879 and 1882. Table 2.1 presents Michelson's determinations minus 299000 in Km/sec. Table 2.1 Velocity of the Light 870 890 850 1000 960 830 880 880 890 910 870 840 740 980 940 790 880 910 810 920 810 780 900 930 960 810 880 850 810 890 740 810 1070 650 940 880 860 870 820 860 810 760 930 760 880 880 720 840 800 880 940 810 850 810 800 830 720 840 770 720 950 790 950 1000 850 800 620 850 760 840 800 810 980 1000 860 790 860 840 740 850 810 820 980 960 900 760 970 840 750 850 870 850 880 960 840 800 950 840 760 780 9...
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This note was uploaded on 08/30/2011 for the course STA 2023 taught by Professor Bagwhandee during the Fall '07 term at University of Central Florida.
 Fall '07
 Bagwhandee

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