Variance (Simply explained)

In statistics, variance measures the deviation from the mean. To calculate the variance, the sum of the squared variances is divided by the number of values.

Variance
The variance now describes the squared average distance from the mean. Because the values are squared, the result has a different unit (just the unit squared) than the original values. Therefore, it is difficult to relate the results.

Difference between variance and standard deviation
So, the difference between the variance and standard deviation dispersion parameter is that the standard deviation measures the average distance from the mean and the variance measures the squared average distance from the mean. Put another way, the variance is the squared standard deviation and the standard deviation is the root of the variance.

Variance Calculator:

More information on variance:

[bradhughes]

I can't put into words how helpful this video is! I'm a working adult taking a data analytics certificate course. I did not do well in high school math because I needed the visual representation and context to make maths meaningful and memorable. If I had videos like this, I might have gone to college. Sincerely, thank you!

[shivdholakia]

I love all your videos. The way you teach with patience, clarity and examples. You are a great teacher.

[nijadhav]

I came across many explanation of variance and SD.
None took the unit in to account. Great explanation.

[inr]

Thank you so much for your clear explanation! Self-learning is made easier for us international students with your help <3

[milonmitra]

I wanted to know about variance from YouTube. Only your video served my purpose.

[Stupid]

It's amazing how easy to understand the teaching is. Thank you

[pradeepkandpal]

Thanks!! Nice explanation. Just a query, shouldn't it be µ as opposed to x bar as it's being calculated for a population. Doesen't affect the logic though but still thought I should bring it to your attention.

[MatthewL]

This channel is so fucking underrated - saved my arse and bailed me out numerous times - appreciate it!

[AllinXavi]

After thinking and ruminating about it for a solid half an hour straight, I think I finally understand. Basically you can’t have the STD (standard deviation) without getting the variance first.

It all goes back to squaring each variables and their variation from the mean individually because we want the variance to be a positive value since a variance of 0 indicates all values are identical, thus you cannot have a variance with a negative value since it would entail nothing but rather a possible error in calculation.

You could just change each individual value where the variation is a negative value, meaning that value falls below the mean value, to a positive value without having to square them to get the STD that way that would be tedious and counterintuitive especially when dealing with much larger sample sizes.

In the end, squaring all values allows every value to be on the same level of measurement, whether with negative or positive variations, prevents having to do tedious guesswork of figuring out which values fall below the mean and changing those that do that have negative variation to positive.

Please tell me I finally got it right 😢

[RAMALHOCORTONDO]

Excellent! I'm using the materials for my students. I'm from Uruguay. Thanks a lot!

[Mabelliot]

thanl you so much! also your accent actually is very soothing so it makes learning easier, the slow pronunciations and stuff. my best math teacher in high school had a similar accent and I was an ace in that class :D!

[arslanasghar]

Bunch of respect for you, my teacher❤

[szamee]

Thanks for this, great explanation. Can elaborate on the reasoning for 1/(n-1)? Why is it (n-1) for sample populations? Why not, say, (n-2) or (n-3.56)? Thanks

[rajanvk]

Hello Data Tab Team. Thank you so much for this wonderful explanation. I now understood it nicely. I have one question regarding the calculation of the position of the median. Why is n/2 used in continuous series and (n+1) /2 is used in discrete series to find median? I will highly appreciate for your explanation

[karunshrestha]

Why don’t we just square root the square unit only ?
It would be interpretable after that right ?

[sundusoomro]

how would you tell a story using both? variance and MAD? what would the story look like? thanks trying to put these in reporting words

[jigdreldorji]

The use of values (individual readings or Xi) to calculate variance is confusing. Just wondering from where those readings 173, 147, 161 etc came from? Kindly watch at 3:41 mins of vedio length. The values could have been (18-155)2 +(8-155)2+(15-155)2 etc...

Hi, can you tell how the value 133 you got should be interpreted in reference to the data .

[vuthihang]

Very helpful and clear! Thanks so much!

[mychanneltest]

Is the quadratic mean important to know? I didn't really understand that tbh.