Calculate Standard Deviation by Hand: Step-by-Step Guide

12.3 In Class Standard Deviation by Hand Name: _______________ A random sample of 30 college students is selected. Each student is asked how much time he or she spent on homework during the previous week. The following times (in hours) are obtained. 19 15 17 18 24 22 21 20 18 20 18, 21, 17, 22, 16, 23, 24, 15, 20, 17, 19, 23, 18, 17, 15, 24, 20, 20, 19, 16 Create a frequency table: 15 16 17 18 19 20 21 22 23 24 3 2 4 4 3 5 2 2 2 3 Find the mean, median, mode and ranges of the data from the table. Mean: 19.9 Median: 19 Mode: 20 Range: 9 Skew?: skew right

12.3 In Class Standard Deviation by Hand Name: _______________ Create a histogram of the data: 9 8 7 6 5 4 3 2 1 15 16 17 18 19 20 21 22 23 24 Find the standard deviation from the data: 1.Find the mean

12.3 In Class Standard Deviation by Hand Name: _______________ 2.Subtract the mean from each piece of data and square the results. 3.Add up all the results, divide by the number of data minus one. (n-1) 4.Take the square root of the result. This is your standard deviation. Mean: 19.9 time frequency Average work SD work Totals 221 15 3 45 3(15-19.27)^2 54.70 7.6 16 2 32 2(16-19.27)^2 21.39 2.7 17 4 68 4(17-19.27)^2 20.61 18 4 72 4(18-19.27)^2 6.45 19 3 57 3(19-19.27)^2 0.22 20 5 100 5(20-19.27)^2 2.66 21 2 42 2(21-19.27)^2 5.98 22 2 44 2(22-19.27)^2 14.91 23 2 46 2(23-19.27)^2 27.83 24 3 72 3(24-19.27)^2 67.12 SD: 2.77

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12.3 In Class Standard Deviation by Hand Name: _______________ Create a normal curve distribution based on your mean and standard deviation. Find the mean, median, mode and ranges of the data from the table. Mean: 2.34 Median: 2 Mode:2 Range: 8 Skew?: skew right Create a histogram of the data. Free Throws # of games 0 7 1 14 2 20 3 11 4 3 5 2 6 1 7 2 8 2

12.3 In Class Standard Deviation by Hand Name: _______________ Standard Deviation Find the standard deviation. 5.Find the mean 6.Subtract the mean from each piece of data and square the results 7.Add up all the results, divide by the number of data minus one. (n-1) 8.Take the square root of the result. This is your standard deviation.

12.3 In Class Standard Deviation by Hand Name: _______________ Mean: 2.34 Free throws # of games average work totals SD 0 7 0 7(0-2.34)^2 38.33 213.89 1 14 14 14(1-2.34)^2 25.14 151.89 2 20 40 20(2-2.34)^2 2.3 12.32 3 11 33 11(3-2.34)^2 4.8 4 3 12 3(4-2.34)^2 8.27 5 2 10 2(5-2.34)^2 14.15 6 1 6 1(6-2.34)^2 13.4 7 2 14 2(7-2.34)^2 43.43 8 2 16 2(8-2.34)^2 64.07 SD: 12.32 Create a normal curve distribution based on your mean and standard deviation.

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12.3 Standard Deviation Done (1)

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