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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