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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.

 

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