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Sum of deviations from median

  1. Dec 26, 2014 #1
    Dear Friends!
    Is sum of deviations from median always minimum,in comparison to deviations from mean,mode or any other observation?Why?
     
  2. jcsd
  3. Dec 26, 2014 #2

    Stephen Tashi

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    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.
     
  4. Dec 27, 2014 #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.
     
  5. Dec 27, 2014 #4

    pwsnafu

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  6. Dec 29, 2014 #5

    statdad

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    OK - I didn't know of any useful minimization property for the mode.
     
  7. Dec 29, 2014 #6
    Thank You Friends!
     
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