How to Calculate Standard Deviation How to Calculate Standard Deviation First, you need to determine the mean. The mean of a list of numbers is the sum of those numbers divided by the quantity of items in the list (read: add all the numbers up and divide by how many there are). Then, subtract the mean from every number to get the list of deviations. Create a list of these numbers. It's OK to get negative numbers here. Next, square the resulting list of numbers (read: multiply them with themselves). Add up all of the resulting squares to get their total sum. Divide your result by one less than the number of items in the list. To get the standard deviation, just take the square root of the resulting number I know this sounds confusing, but just check out this example: your list of numbers: 1, 3, 4, 6, 9, 19 mean: (1+3+4+6+9+19) / 6 = 42 / 6 = 7 Know More About Homework Help Math.Tutorvista.com
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list of deviations: -6, -4, -3, -1, 2, 12 squares of deviations: 36, 16, 9, 1, 4, 144 sum of deviations: 36+16+9+1+4+144 = 210 divided by one less than the number of items in the list: 210 / 5 = 42 square root of this number: square root (42) = about 6.48 So six straightforward steps on how to find Standard Deviation ;1. Get the Mean 2. Get the deviations 3. Square these 4. Add the squares 5. Divide by total numbers less one 6. Square root of result is Standard Deviation -------------------------------------------SO STEP BY STEP;1. get the Mean to begin you need the mean or the average, for example add 23, 92, 46, 55, 63, 94, 77, 38, 84, 26 ... = 598 divide by 10 (the actual number of numbers) 598 divided by 10 = 59.8 so the mean or average of 23, 92, 46, 55, 63, 94, 77, 38, 84, 26 is 59.8 ____________________________________________________ 2. get the deviations subtract the mean from each of the numbers, the answers are;-36.8, 32.2, -13.8, -4.8, 3.2, 34.2, 17.2, -21.8, 24.2, -33.8 Learn More Free Online Math Tutor Math.Tutorvista.com
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3. square these to square means multiply them by themselves, the answers are;1354.24, 1036.84, 190.44, 23.04, 10.24, 1169.64, 295.84, 475.24, 585.64, 1142.44 4. add the squares total of these numbers is 6,283.60 5. divide by total number of numbers less one;you had 10 numbers less 1 is 9 numbers so 6283.60 divided by 9 = 698.18 6. square root of result is Standard Deviation square root is the number multiplied by itself to get 698.18 which is:26.4 so 26.4 is the Standard Deviation...
Ok so above is the manual method of doing this ...below is the step by step example using Excel...
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