Measures of Spread: Crash Course Statistics #4

Today, we're looking at measures of spread, or dispersion, which we use to understand how well medians and means represent the data, and how reliable our conclusions are. They can help understand test scores, income inequality, spot stock bubbles, and plan gambling junkets. They're pretty useful, and now you're going to know how to calculate them!

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[kennethfoster]

You explained in 30 seconds the intuition behind variance. In 4 years my college professors could only regurgitate the formula to me.

[verdatum]

Kudos to whoever did the background for this course. It looks great; one of my favorites yet. Edit: Kudos to Dave Freeman. Yay for end credits!

[horizon]

Love the inverted bell curve scar on her forehead instead of a lightning bolt scar in the thought bubble sequence. Makes me think she was almost killed by some deranged math professor but was saved by the power of statistical analysis.

[lukehebert]

Using this playlist as a primer before diving back into the world of statistics after changing careers. This is super helpful! I especially loved the visualization of variance with the squares :)

[Anaguma]

A detailed explanation or example of how dividing the variance by n as opposed to n-1 biases the calculation would be nice.

This never got explained in any of the statistics courses I've taken.

[iAmTheSquidThing]

Square wins makes perfect sense. You will often hear people claim that they have won fair and square.

[bandanawaddledee]

Amazing explanations. Really cleared up my questions about my statistics class. One small suggestion though. Could you please include the formulas to calculate Variation, Standard Deviation, etc. It would mean a lot to me. Thank You!

[simonclarke]

This is absolutely brilliant - I am a physician looking to do a PhD and my last formal maths course was at high school (shall we say 30+ years ago...). I REALLY needed to go back to basics on statistics and this course is perfect. I feel set up to attack the more specialised texts on medical stats as you have explained the principles behind the formulae... thankyou!! I have one minor point, it would have been useful to mention why you square the deviation of each data point when calculating the variance; it took my rusty brain quite a while to realise that all of the deviations above and below the mean would otherwise cancel themselves out!

[deniseyang]

the best crash course video i've seen by far. thank you for putting standard deviation into perspective!

[najrenchelf]

We started having Statistics as a subject starting last week. This series’s timing is amazing!

[atlaswar]

I love that ending! I will no longer consider myself as part of the average!

[luisfdconti]

She's a blood purist! Muggle borns can fly as well as anyone!

[valentinhuiban]

I am trying to prepare for a resit exam for my statistics course which was so confusing. I want to say that this crash course is a blessing, and especially this episode which has done a marvelous job on explaining variance and deviation and more important what is the standard and why, more than my uni could. Thank you!

[OlleLindestad]

This video contains an important misconception! :O

Namely, that the standard deviation is the average of the deviations from the mean. Actually, because half of all deviations are negative (below the mean) and the other half are positive (above the mean), *the average of all deviations is always zero.* This is in fact why we square the deviations when calculating the variance - squares are always positive, so this gets rid of the problem.

Of course, you could simply average the sizes of the deviations, disregarding the plus or minus signs. The resulting value is called the absolute mean deviation, and it's similar to the standard deviation, but *not the same*. Also, for historical and practical reasons, the absolute mean deviation is almost never used.

[ganaraminukshuk]

And never forget the standard deviation.

[moonemonne]

Totally didn't expect a statistics lesson teach me some life lesson. Thanks for your kind words!

[mosama]

Guys just a quick note, if you're still confused about the variance and standard deviation Khan Academy has a very nice explanation for it.

[ReaperVXG]

Phenomenal videos and narration by Adrian, certain terminology is assumed and challenging to understand but it is afterall a "Crash Course"

[ruslanakhmedagaev]

Math is everywhere! :) Please, make the Crash Course Mathematics; it would be a pleasure to watch these series.

[dinornis]

I've been trying to wrap my head around standard deviation for a while now and was always confused by it. This video lead me to that 'aha!' moment where I finally get it -- thank you!