Question 1161931: The variance of the data
{17, 15, 23, 7, 9, 13} is
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
List them and add them
X
--
17
15
23
7
9
13
--
84
Divide the sum, 84, by the number of values, which is 6:
X
--
17
15
23
7
9
13
--
6)84
14 <-- that's the mean
Subtract the mean, 14, from each value.
If you add them, the sum will always be 0
X X-14
-- -----
17 3
15 1
23 9
7 -7
9 -5
13 -1
-- ---
6)84 0
14
We square each number in that list, then add them:
X X-14 (X-14)²
-- ----- -------
17 3 9
15 1 1
23 9 81
7 -7 49
9 -5 25
13 -1 1
-- --- ------
6)84 0 166
14
Then we divide that sum, 166, by 1 less than the number of numbers,
which is 6-1 or 5:
X X-14 (X-14)²
-- ----- -------
17 3 9
15 1 1
23 9 81
7 -7 49
9 -5 25
13 -1 1
-- --- ------
6)84 0 5)166
14 33.2 <--variance
[If we wanted the standard deviation we would take the square root
of the variance. So the standard deviation is 5.761944116.]
Answer: the variance is 33.2
Edwin
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