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

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- Thread starter gianeshwar
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- #1

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

- #2

Stephen Tashi

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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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[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.

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Thank You Friends!

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