Pearson's Skewness

Aldo

Hiya, I am studying Human Geography and thanks to some wicked twisted mind we have to learn how to measure the skewness of a probability distribution. Thank god we're following Pearson on this, instead of the "real" formulae.

However, Pearson gives 2 different calculations:

* (mean - mode) / standard deviation
* 3 (mean - median) / standard deviation

My university uses the latter, so I will be using that for my assignment, however, no one has ever bothered explaining me why there's a 3 in front of that formula. :? This makes me wonder why I should multiply the (mean - median) by 3. I can't think of a logical explanation myself, so here I am.

Wiki: http://en.wikipedia.org/wiki/Skewness .

tl;dr: Why is there a 3 in 3 (mean - median) / standard deviation ?

grug

I am studying human geography, too LET ME CHECK OUT YOUR MOUNTAINS BABY, YEAH LET'S GO TO TASMANIA YEAH

YEAH


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Aldo

Well, that's something I wasn't expecting. :<

Thanatos

Well, the definition for the standard deviation is based on the approximate distance from the median you have to go to encompass 98% of responses (two standard deviations, both directions). So you probably have to multiply by three because otherwise the number is too small.

Yes, it's arbitrary. But this is statistics; it's all pretty arbitrary.

BlazeFire

Now, my prof kinda sucks but isn't the definition of standard deviation the square root of variance, which is something whose equation I don't want to try to write out in text but involves E(x^2) - mean^2? Or is that a result from the standard deviation being defined as you say?

Thanatos

BlazeFire wrote:

Now, my prof kinda sucks but isn't the definition of standard deviation the square root of variance, which is something whose equation I don't want to try to write out in text but involves E(x^2) - mean^2? Or is that a result from the standard deviation being defined as you say?

You're talking about the mathematical definition, I'm talking about the practical definition. The OP was talking about using different formulae for figuring it out, which I've never heard of (I've only heard of the one you're using), but I don't see any reason why you couldn't get an approximation of it another way, if that's what your professor wants you to do.

Aldo

Thanks Than, that should be it. @_@;

Or rather, that's the only logical thing that came to mind, since the skewness is normally described as a value close to zero, so maybe that was just "needed" to make it easier to fiddle around with.

question answered~!
*cue Final Fantasy Victory song*

piL

I'm not sure about this (even though you say it's answered), but the mode will be the highest point on the curve. Closer to the mean will be the median, which, in the case of a skew, will always be on the side of the mode closer to the mean. In effect, what I'm saying is that the mode's distance is a more signifigant indicator of how skewed the graph is, and the multiplier is to more or less even out this difference.

This is my conjecture, but seems right to me.