[TowerTalk] Median vs Average

Roger (K8RI) on TT K8RI-on-TowerTalk at tm.net
Sun Aug 9 16:30:00 EDT 2015


That is true for small samples, but not those large enough to be 
statistically significant.
The larger the sample, the more accurate statistically.  With 
lightening, 5 to 10% of the number of measured samples including 
outliers would be appropriate.  Even 5% would be a large number where 
the outlier would have more of an effect on the median, than the 
average.  IE, one super strike (positive lightening) which could be  5 
or more times the typical strike would raise the median substantially, 
but have virtually no effect on the average.  Population surveys with 
margins of error of +/- 3% should contain thousands of samples.
At least that's what we were taught in CS and Math.

73

Roger (K8RI)



On 8/9/2015 6:28 AM, kr2q at optimum.net wrote:
> I was recently stated here that:
>
> [snip]
> With a number of samples large enough to be statistically valid a single, significant outlier, be it
> high or low can substantially skew the median, but have little effect on the average.
> [end snip]
>
> Ummm.  This is exactly backwards.  The median is often used because it is immune to outliers,
> whereas the mean (average) is can be greatly impacted by the outliers.
>
> EG: Grades in class.  Lets say your grades are 95, 95, 95, 95, 95, 95, 95, 95, 95, 95.
>
> What grade is typical?  Well, 95!  The mean (average) is 95 and the median is 95.
>
> But what if you failed one quiz/test and got a 15?
> Now your grades are 95, 95, 95, 15, 95, 95, 95, 95, 95, 95.
>
> Your median grade is still 95, but your average is now 87.
>
> So clearly, median was unaffected by an outlier, while the average moved a lot.
>
> If you make "n" larger, you will still see the same thing; median is static while average isn't.
>
> For those who "love" using the mean (average), try using the geometric mean.  It greatly
> lessens the impact of outliers.  Of course, you have to account for that when reporting out.
>
> de Doug KR2Q
>
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-- 

73

Roger (K8RI)


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