Results 1 to 5 of 5

Math Help - mean absolute variation

  1. #1
    Newbie
    Joined
    Aug 2009
    Posts
    3

    mean absolute variation

    Hi everyone,

    Sorry if this question is too random or general, but itīs bugging me.

    Why do we write the mean absolute variation like this:


    <br />
\psi=\frac {1}{N} \sum_{i=1}^N|x_i-\mu|<br />


    and not like this?:


    <br />
\psi=\frac {\sum_{i=1}^N|x_i-\mu|}{N} <br />


    i.e. why do we multiply the sum of deviations by 1/N, instead of just dividing the sum of deviations by N?


    Thanks
    Last edited by Occurin; August 24th 2009 at 04:38 PM. Reason: figured out latex
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2009
    Posts
    591
    Quote Originally Posted by Occurin View Post

    ...

    why do we multiply the sum of deviations by 1/N,
    instead of just dividing the sum of deviations by N?

    ...
    It looks to me as if it's the same.
    Could you explain the difference, please?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2009
    Posts
    3
    Aidan,

    Sorry, I wasnīt clear... they are the same, which is my point. The first one seems to me to add another layer of non-intuitive complexity that bugs beginners like me... I wondered if there was a purpose to it that I havenīt caught.

    Thanks for replying.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by Occurin View Post
    Hi everyone,

    Sorry if this question is too random or general, but itīs bugging me.

    Why do we write the mean absolute variation like this:


    <br />
\psi=\frac {1}{N} \sum_{i=1}^N|x_i-\mu|<br />


    and not like this?:


    <br />
\psi=\frac {\sum_{i=1}^N|x_i-\mu|}{N} <br />


    i.e. why do we multiply the sum of deviations by 1/N, instead of just dividing the sum of deviations by N?
    The difference is not mathematical but typographical: the version with 1/N looks more elegant and takes up less space. Back in the days of manual typesetting, printers hated large build-up fractions, and encouraged copy-editors and authors to avoid them where possible. Now that everyone uses TeX, that's not so much of an issue, but old preferences linger on.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Aug 2009
    Posts
    3
    Thanks a lot, Opalg, thatīs exactly the kind of explanation I was looking for.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: September 7th 2011, 07:11 AM
  2. Replies: 8
    Last Post: May 23rd 2010, 10:59 PM
  3. finding absolute maximum and absolute minimum
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 15th 2009, 04:22 PM
  4. Replies: 2
    Last Post: November 8th 2009, 01:52 PM
  5. Find the absolute maximum and absolute minimum
    Posted in the Calculus Forum
    Replies: 5
    Last Post: December 12th 2008, 09:46 AM

Search Tags


/mathhelpforum @mathhelpforum