1. ## mean absolute variation

Hi everyone,

Sorry if this question is too random or general, but it´s bugging me.

Why do we write the mean absolute variation like this:

$
\psi=\frac {1}{N} \sum_{i=1}^N|x_i-\mu|
$

and not like this?:

$
\psi=\frac {\sum_{i=1}^N|x_i-\mu|}{N}
$

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

Thanks

2. Originally Posted by Occurin

...

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?

3. Aidan,

Sorry, I wasn´t 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 haven´t caught.

4. Originally Posted by Occurin
Hi everyone,

Sorry if this question is too random or general, but it´s bugging me.

Why do we write the mean absolute variation like this:

$
\psi=\frac {1}{N} \sum_{i=1}^N|x_i-\mu|
$

and not like this?:

$
\psi=\frac {\sum_{i=1}^N|x_i-\mu|}{N}
$

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.

5. Thanks a lot, Opalg, that´s exactly the kind of explanation I was looking for.