Question

Here is a distribution of 6 observations, sorted in ascending order:

4.7, 9.2, 10.9, 12.3, 16.6, 18.3

The mean of this distribution is 12. What is the value of ? 6 sigma (xi-x with the line above it)

Answer 1

sigma as in: o~ ?

Answer 2

no the one that looks like a capital E

Answer 3

\[\sum(xi-\bar x)\]

Answer 4

Yes!

Answer 5

0

Answer 6

i take it this is more properly:
\[\sum_{i=1}^{6}(x_i-\bar x)\]

Answer 7

Yes that is the correct equation

Answer 8

it should, as zarkon states, be zero

just subtract the mean from your vaoues and add up the totals

Answer 9

values that is

Answer 10

4.7 -12 = -7.3
9.2 -12 = -2.8
10.9 -12 = -1.1
12.3 -12 = .3
16.6 -12 = 4.6
18.3 -12 = 6.3
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Answer 11

\[\sum_{i=1}^{n}(x_i-\bar x)\]

\[=\sum_{i=1}^{n}x_i-\sum_{i=1}^{n}\bar x\]

\[=\sum_{i=1}^{n}x_i-n\bar x\]

\[=\sum_{i=1}^{n}x_i-n\frac{\sum_{i=1}^{n}x_i}{n}\]

\[=\sum_{i=1}^{n}x_i-\sum_{i=1}^{n}x_i=0\]