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)

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)

amistre64 · Answer

sigma as in: o~  ?

anonymous · Answer

no the one that looks like a capital E

amistre64 · Answer

$$\sum(xi-\bar x)$$

anonymous · Answer

Yes!

zarkon · Answer

attachment

amistre64 · Answer

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

anonymous · Answer

Yes that is the correct equation

amistre64 · Answer

it should, as zarkon states, be zero

just subtract the mean from your vaoues and add up the totals

amistre64 · Answer

values that is

amistre64 · Answer

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
----------------

zarkon · Answer

$$\sum_{i=1}^{n}(x_i-\bar x)$$

$$=\sum_{i=1}^{n}x_i-\sum_{i=1}^{n}\bar x$$

$$=\sum_{i=1}^{n}x_i-n\bar x$$

$$=\sum_{i=1}^{n}x_i-n\frac{\sum_{i=1}^{n}x_i}{n}$$

$$=\sum_{i=1}^{n}x_i-\sum_{i=1}^{n}x_i=0$$