Statistics - Standard Deviation, Standard Error and Mean

[Learn]

Hello,

Just had a question regarding statistical analysis.

I'm trying to calculate the average of 4 numbers from a data set of 6 numbers in excel without manually choosing to average only the 4 numbers.

e.g.


85 20 32 45 27 3 (total mean = 35.3 desired mean = 31)
100 30 27 40 21 1
...etc

The middle 4 numbers represent a more realistic result whilst the two end numbers are irrelevant.

I've tried looking into weighted averages however I'm unsure how to apply this to an excel sheet.

I'd prefer to find a formula which would discount numbers which vary wildly from the average amount and focus only on the few that don't.

Any help would be greatly appreciated.

 

[Simon Bridge]

You have six numbers - if you picked four of them at random, what would be their average?
That about it?

Clearly that depends on the four numbers - but you can work out each possible combination of 4, and work out the average for each one. The expectation value of the averages will be your answer.

 

[DrDu]

A better strategy than excluding observations arbitrarily would be to compute "robust" estimates of the distribution, e.g. the median instead of the mean and the median absolute deviation (MAD) as an estimator for the variability.
See
http://en.wikipedia.org/wiki/Robust_statistics

 

[Bacle2]

As a general comment, to reinfoce what was already said, in distributions that are not symmetrical or not unimodal, and or distributions with outliers, the variance is not a good measure of spread. You may also want to represent your data with a dot plot or stemplot:

http://en.wikipedia.org/wiki/Stem-and-leaf_plot