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Statistics Chapter 12

Statistics Chapter 12. 1. Measures of Dispersion Section 12.3. 2. Measures of Dispersion. The range of a set of numbers is the difference of the greatest and the least of the numbers in the set. Let a set of n numbers be denoted by X 1 , X 2 , X 3 ,…, X n and

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Statistics Chapter 12

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  1. StatisticsChapter 12 1

  2. Measures of DispersionSection 12.3 2

  3. Measures of Dispersion • The range of a set of numbers is the difference of thegreatest and the least of the numbers in the set. • Let a set of n numbers be denoted by X1, X2, X3,…, Xn and • let themean of these numbers be denoted by . Then thestandard deviation s is given by 3

  4. Example Find the range and the standard deviation s, to two decimal places, for 3, 5, 8, 13, and 21. range = 21 – 3 = 18 4

  5. Alternative Procedure 5

  6. Example • Out of 10 possible points, a class of 20 students made the following test scores: • 0, 0, 1, 2, 4, 4, 5, 6, 6, 6, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10 • What is the mean? • Calculate the standard deviation tothe nearest hundredth. • What percent of the scores lie withinone standard deviation from themean? 6

  7. Solution a. = 120/20 = 6 7

  8. Solution Continued The interval of one standard deviation from the mean is 6  3.23 = 2.77 to 6 + 3.23 = 9.23. 0, 0, 1, 2, 4, 4, 5, 6, 6, 6, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10 There are fourteen scores highlighted in red that are within 1 standard deviation from the mean. c. 14/20 = 0.7 = 70% of the scores are within 1 standard deviation from the mean. 8

  9. Example The daily numbers of pounds of garbage for six different households were 6, 2, 17, 3, 5, and 9 pounds. Find the interval of one standard deviation from the mean. The interval of one standard deviation from the mean is 7.00  5.48 = 1.52 to 7.00 + 5.48 = 12.48 9 END

  10. How to calculate mean , median, and standard deviation at the same time using a TI-82, TI-83, or TI-84 Press 2nd + 4 enter: This clears the list and should be done before entering new data Click on STAT button Select (press enter) Edit Enter the scores under L1 so that L1(1) = 1st score, L1(2) = 2nd score etc. Click on STAT button again Move cursor to CALC Select 1-Var Stats, press enter See results = mean and Sx = standard deviation Note: If you look at this screen you will notice an arrow pointing downward with the letter n next to it. The number associated with n is the number of scores that was entered. If you scroll downward you will eventually see the median value.

  11. Binomial Experiment n = number of times the experiment is to be preformed p = probability of success Example

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