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Topic: properties of measures of central tendency
Replies: 5   Last Post: Apr 22, 2016 7:15 PM

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Gordon Sande

Posts: 137
Registered: 5/13/10
Re: properties of measures of central tendency
Posted: Apr 22, 2016 1:32 PM
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On 2016-04-22 14:36:47 +0000, said:

> Suppose you have some real valued measurements of something.
> (1) The mean minimizes the sum of squared deviations of each
> observation from it.
> (2) The average of the largest and smallest observation minimizes the
> maximum absolute value of the deviation from it.

Otherwise known as the midrange.

> (3) Do other measures of central tendency such as the median have a
> similar property?

The median minimizes the sum of absolute deviations. Otherwise known as
the L_1 fit.

> (4) Is there a closed form formula for the point that minimizes the sum
> of the absolute value of the deviations from it?

Oterwise known as the median.

Before you even ask, yes there are versions of regression for the
various norms.

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