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Standard Deviation, Variances and Means

posted Feb 4, 2010, 2:39 PM by Prof Kiernan   [ updated Feb 6, 2014, 5:58 AM ]

Weighted means, Standard deviations, and variances

Using just one list:

1. First put values in the X list and get a total

 X 18 18 20 19 21 19 22 21 25 28 24 18 19 20 19 19 21 19 22 32 36 28 total: 488

2. find the mean (average):

NOTE: Don’t panic about the notation, there are multiple ways of writing mean.

3. Subtract the mean from every value in the x column:

 X x-mean 18 18 -22.2 = -4.2 18 18 -22.2 = -4.2 20 20 -22.2 = -2.2 19 19 -22.2 = -3.2 21 21 -22.2 = -1.2 19 19 -22.2 = -3.2 22 22 -22.2 = -0.2 21 21 -22.2 = -1.2 25 25 -22.2 = 2.8 28 28 -22.2 = 5.8 24 24 -22.2 = 1.8 18 18 -22.2 = -4.2 19 19 -22.2 = -3.2 20 20 -22.2 = -2.2 19 19 -22.2 = -3.2 19 19 -22.2 = -3.2 21 21 -22.2 = -1.2 19 19 -22.2 = -3.2 22 22 -22.2 = -0.2 32 32 -22.2 = 9.8 36 36 -22.2 = 13.8 28 28 -22.2 = 5.8 total: 488

4. square the x-mean column and get the total of the column:

 X x-mean (x-mean)2 18 18 -22.2 = -4.2 17.64 18 18 -22.2 = -4.2 17.64 20 20 -22.2 = -2.2 4.84 19 19 -22.2 = -3.2 10.24 21 21 -22.2 = -1.2 1.44 19 19 -22.2 = -3.2 10.24 22 22 -22.2 = -0.2 0.04 21 21 -22.2 = -1.2 1.44 25 25 -22.2 = 2.8 7.84 28 28 -22.2 = 5.8 33.64 24 24 -22.2 = 1.8 3.24 18 18 -22.2 = -4.2 17.64 19 19 -22.2 = -3.2 10.24 20 20 -22.2 = -2.2 4.84 19 19 -22.2 = -3.2 10.24 19 19 -22.2 = -3.2 10.24 21 21 -22.2 = -1.2 1.44 19 19 -22.2 = -3.2 10.24 22 22 -22.2 = -0.2 0.04 32 32 -22.2 = 9.8 96.04 36 36 -22.2 = 13.8 190.44 28 28 -22.2 = 5.8 33.64 total: 488 493.28

5.Plug and chuck:

To get the Variance:

AKA: Divide the total of the (x-mean)2 column by the sample size minus 1

Standard Deviation:

AKA: get the square root of what you get from the variance formula.

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Prof Kiernan,
Nov 22, 2010, 3:05 PM