1. 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:

$
\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 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.

4. Originally Posted by Occurin
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:

$
\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, thatīs exactly the kind of explanation I was looking for.