Thread: 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:





and not like this?:





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


Thanks

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?

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.

Thanks for replying.

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:





and not like this?:





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.

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