Sum of deviations from median

  • Thread starter gianeshwar
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  • #1
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Main Question or Discussion Point

Dear Friends!
Is sum of deviations from median always minimum,in comparison to deviations from mean,mode or any other observation?Why?
 

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  • #2
Stephen Tashi
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Dear Friends!
Is sum of deviations from median always minimum,in comparison to deviations from mean,mode or any other observation?Why?
I assume you're talking about the sum of the deviations of the values in a sample from a statistic computed from a sample. The sum of the deviations of sample values from the sample mean is zero.
 
  • #3
statdad
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A median minimizes this sum (in a sample) as a function of [itex] a [/itex]
[tex]
\sum_{i=1}^n |x_i - a|
[/tex]

The mean (sample average if you will) minimizes this sum as a function of [itex] a [/itex]
[tex]
\sum_{i=1}^n \left(x_i - a\right)^2
[/tex]

I don't know of any minimizing property for the mode.
 
  • #4
pwsnafu
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  • #5
statdad
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OK - I didn't know of any useful minimization property for the mode.
 
  • #6
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Thank You Friends!
 

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