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

 Messages: [ Previous | Next ]
 Gordon Sande Posts: 137 Registered: 5/13/10
Re: properties of measures of central tendency
Posted: Apr 22, 2016 1:32 PM

On 2016-04-22 14:36:47 +0000, analyst41@hotmail.com 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.

Date Subject Author
4/22/16 analyst41@hotmail.com
4/22/16 Richard Ulrich
4/22/16 analyst41@hotmail.com
4/22/16 Gordon Sande
4/22/16 analyst41@hotmail.com
4/22/16 Gordon Sande