3-2 Exercise Measures of Average and Measures of Deviation

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Southern New Hampshire University **We aren't endorsed by this school
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PSY 223
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Statistics
Date
Aug 23, 2023
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3
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3-2 Exercise: Measures of Average and Measures of Deviation 1 3-2 Exercise: Measures of Average and Measures of Deviation Krista Wehr Southern New Hampshire University
3-2 Exercise: Measures of Average and Measures of Deviation 2 Exercise 14: Perception of Time (Section 4.1: p. 125) 14. Perception of Time. The data below are times (in seconds) recorded when statistics students participated in an experiment to test their ability to determine when 1 minute (60 seconds) had passed. What do these data suggest about students' perception of time? 53 52 75 62 68 58 49 49 A. The mean is when all numbers in the data set are added together, total is found, and then divided by the whole data set. The mean is 58.25 for the data set . a. Mean = 53+52+75+62+68+58+49+49 = 466 (x) X 8 (n) = 58.25 seconds B. Median is the number that is the center of the data set since there is an even number, we take the two middle numbers and then divide them by two. The median is 55.5 for the data set . a. Median = 49 49 52 53 58 62 68 75 = 53+58 = 111X2 = 55.5 seconds C. The mode is the number that is repeated the twice in the data set, so the mode is 49 for the data set . a. Mode = 53 52 75 62 68 58 49 49 = 49 seconds. Exercise 13: Perception of Time (Section 4.3: p. 145) 13. Perception of Time. The following times (in seconds) were recorded when statistics students participated in an experiment to test their ability to determine when 1 minute (60 seconds) had passed: 53 52 75 62 68 58 49 49
3-2 Exercise: Measures of Average and Measures of Deviation 3 A. The range is between the highest and lowest values, so the range is 26 of the data set a. Range = 53 52 75 62 68 58 49 49 = 75-49 = 26 seconds. B. The standard deviation is found when the average of all deviations from the mean, so the standard deviation is 9.467 of the data set. a. Step 1. Deviation from mean = data value - mean 49 - 58.25 = 9.25 49 - 58.28 = -9.25 52 - 58.25 = -6.25 53 - 58.25 = -5.25 58 - 58.25 = -0.25 62 - 58.25 = 3.75 68 - 58.25 = 9.75 75 - 58.25 = 16.75 b. Step 2 49 = 85.5625 49 = 85.5625 52 = 39.0625 53 = 27.5625 58= 0.0625 62 = 14.0625 68 = 95.0625 75 = 280.5625 c. Step 3. = 627.5 Step 4. 627.5 / 7 = 89.64285714 Step 5. Standard Deviation = 9.467991188 seconds per or 9.47 seconds.
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