Statistics Chapter 12 1

Measures of Dispersion Section

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 let the mean of these numbers be denoted by. Then the standard deviation s is given by 3

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

Alternative Procedure x 3  7   Total

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

a. = 120 / 20 = 6 Solution x frequency fxf 020 6 5 4 2 1 Total20120Total198 7

Solution Continued The interval of one standard deviation from the mean is 6  3.23 = 2.77 to = , 1, 2, 4, 5, 6, 7, 8, 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.

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. 9 The interval of one standard deviation from the mean is 7.00  5.48 = 1.52 to = END

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 1)Click on STAT button 2)Select (press enter) Edit 3)Enter the scores under L1 so that L1(1) = 1 st score, L1(2) = 2 nd score etc. 4)Click on STAT button again 5)Move cursor to CALC 6)Select 1-Var Stats, press enter 7)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.

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