Introduction to the normal distribution | Probability and Statistics | Khan Academy

Exploring the normal distribution

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[SomebodyOutThre]

Guys I found this amazing explanation in another video's comment section, I hope it helps!

"It took me a while to understand this and had to rewatch this video a few times, but essentially there are ground rules for calculating standard deviation. Standard deviation is saying something like "Math test scores averaged 92 'give or take' 3 points".

So 92=mean, deviation=3 (the give or take number), so 92-3 and 92+3 means that 68.26% of all students score fell within 89-95 (92-3=89 or 92+3=95). this is "1 standard deviation".

This video is using the ground rules for calculating standard deviation. Since standard deviation is a mathematical formula, the existing ground rules dictate that you have a 68.26% of all test scores to be within 1 standard deviation (3 points in my example).

So for 2 or 3 standard deviations, you use the same formula above, but instead of 3, use 6 (2 stDevs) or 9 (3 stDevs)

1 stDev = 68.26% probability (give or take 3 points)
2 stDev = 95.44% probability (give or take 6 points)
3 stDev = 99.7% probability (give or take 9 points)

NOTE: The 68.26%, 95.44%, 99.7% are existing rules used for normal distribution and apply to any example."

[MidnightFreefall]

I just wanted to say that I'm taking statistics while studying to be a veterinarian. The course at uni is very brief, nothing goes into too much detail on why certain things work the way they do. This playlist is a godsend. I love maths, and I love how passionate you are about these topics. Thank you for helping me study!

[matrixmodal]

I find it very effective that you *repeat* the same ideas over and over again! It reinforces them.

[basschipper]

Ten years later, still relevant. Sal you are a gift from God

[alexkuligowski]

The connection between the normal distribution and the cumulative distribution function just clicked! Thank you! I see the normal distribution as the distribution to explain most natural phenomenon if we use the law of large numbers to arrive at the central limit theorem. The cumulative distribution function is nothing more than the sum of the probability from negative infinity to a given X of interest. After seeing how this comes together the way we use the cdf to obtain an interval of probability along a continuous distribution is super slick.


Last note: I've always wondered why we have an index of pages for the normal distribution. After the small note on how difficult the integral would be of the equation for a normal curve it makes so much more sense why these tables in all statistics books I've ever looked in the back of.


Cheers!

[adnanhossain]

i dropped out of engineering and joined business school just so i dont ever have to see that GOD DAMN INTEGRATION SIGN... but... we meet again. my old foe!

[hussainrangwala]

I wish I had watched this video earlier during my engineering.. Mr. Sal Khan take a bow!! this is how you teach something to someone..

[khanacademy]

the normal distribution is a class of distributions that have the same basic shape but different means and std deviations. Human height is probably close to a normal distribution with the mean around 5'6 (somewhere in between men and women average).

[lobsterofficial]

11 years later and you made me understand what the normal distribution is all about for my Biomed Technology class thank you Khan <3

[McNoat]

I very much enjoyed the transformation of the formula into different "forms". I think this helps to reduce the fear that comes (for me) from looking at so many symbols and makes it a bit more palpable.

[donnajoe]

The only slight mistake was at 15:55. You were supposed to enter 10 and not 100 i.e e^-1/2(x+5/10)^2. This was a good explanation.

[randompotato]

there is a small fault when you wrote down the fonction to integrate where the mean is -5 and the standard deviation is 10 you wrote ((x+5)/100)^2 the right expression would be ((x+5)/10)^2 or (x+5)^2/100) otherwise you have (x+5)^2/(the standard deviation)^4

[tseringangle]

Thank you! It made so much more sense now. That graph representation and manipulating equation made it more easy to understand reason behind all.

[akanshaw]

Glad I decided to watch this video before starting to study for test !! Helped a lot !

[Jonny-uuwf]

I find these videos really helpful. Got a statistics exam tomorrow, been revising off these for the past few weeks. This video is not very good though. Really confusing. 

[JoshMolina]

Thanks to Sal and staff at Khan, I'm able to throw down with the quants at the bank. Thanks guys!!!

[sasamuraki]

wow, that part of linking normal distri to 'nothing is impossible, but the probability matters' is awesome.. deep...

[pradeepknal]

thanks a ton for all the teachers and staff team at Khan Academy!

[matthewa]

this is deep.
How are pi and e and chance related in this way!

My mind is blown right now.

I discovered the norm dist. in uni in like 2007 but only now have a greater appreciation for it.

Just number plugged in the past. This mathematical model is truly beautiful to me.

[Timmytimmy]

15:54 There is a mistake here.
Sal wasn't supposed to square the entire ((x+5)/100), he was just supposed to square (x+5) since the deviation was already squared from 10 to 100.