Standard deviation (simply explained)

The most common measures of dispersion for metric variables are the standard deviation and the variance in statistics. These two measures relate each expression of a variable to the mean and indicate how much the individual expressions scatter around the mean.

What is the standard deviation and how do I calculate it?
In statistics, the standard deviation gives you the spread of a variable around its mean. The standard deviation, is the average distance of all measured values of a variable from the mean of the distribution.
The measure of dispersion standard deviation thus indicates how much the individual values scatter around the mean value. If the individual values scatter strongly around the mean, the result is a large standard deviation of the variable.

Sorry, in the example of course a standard deviation of 11.50 comes out and not 12.06!!!!

► Calculate the standard deviation online

► E-BOOK

► Tutorial standard deviation and descriptive statistics
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0:00 Introduction
0:22 What is the standard deviation?
2:16 How do I calculate the standard deviation?
4:09 Why are there two formulas?
5:59 What is the difference with variance?
7:17 Calculate the standard deviation online.

[rdjwpvi]

Thank you random german woman on the internet. You don't understand how much this help me to go through my finals 😭 God bless you :)

[norencezyron.bedasua]

I don't understand why anyone would height this video. That was very clearly explained. Thanks!

[magiciansway]

Many thanks. I am 62 and this is the first time I have a clear understanding of standard deviation. I also feel happy hearing you happy demeanor. Thanks.

[WilliamAlanPhoto]

It's a bold social experiment to calculate the standard deviation of hate. I salute you.

[johnieday]

As a psychology student I'm a bit dense when it comes to numbers and I need to know them. This really helped me keep up the good work and thank you!

[lauramandea]

I have a statistic test in a couple days and this video explained everything that i didn't understand in a month in just 7 minutes. thank you from Italy

[robindhood]

I kept hearing “hate” every time she said height; thankfully there were visuals. Great video and explanation, now I’m off to get my hearing checked.

[nizar]

You have explained very clearly and slowly to make understand us! Thank you a lot! 👍

[kimbott]

Love how simple and straightforward this video is. I'd love if it included why we use the n-1 in a sample case. I realize that would add significantly to the length of the video but it's conceptually pretty cool and a useful thing for more people to think about.

[LalitKumar-njxc]

Clarity and pace of your voice is making it very easy to understand.

[lauterunvollkommenheit]

0:40 "Let's say you measure the hate of a small group of people" - I've done it many times, mostly by accident.

[vasQpr]

Finally someone managed to explain it to me successfully

[tarunaggarwal]

one of the best-detailed example, I have ever seen....i dint think I will ever forget this

[tchen]

This is the first time I ever understand the concept of standard deviation and its purpose. Thank you so much for this helpful content!

[ianchikopela]

Ma'am, you are awesome. The simplicity exeh!
Usually people come to YouTube when in dire need of simple, straightforward, i-am-dumb step-by-step explanations. And you, you just did that. You just provided that. YOU AWESOME!

[musicsang]

Ma'am I pray to God that you live long and achieve whatever is best in your life. You are such a knowledgeable person who help us a lot. Thanks a lot. A big salute to you.

[jgostling]

Excellent presentation, clear and concise. The only thing I miss is an explanation of WHY the standard deviation of a sample is divided over "n-1", as opposed to dividing over "n" as is the case for the whole population. This is something I've never quite understood.

[blackviking]

Hands down the best and most succinct explanation of std dev I've ever seen.

[piotrrybka]

Nice video, but what is missing are answers to the following questions:

Why in standard deviation we use quadratic mean instead of absolute value and arithmetic mean. What is the advantage of using quadratic mean? And why quadratic and not cubic? Or fourth power? Tenth power would also look nice and could be easier to remember. You say that it would be always zero, but that is not possible if absolute value was used. In your example the arithmetic mean of all height deviations is 10.(6).

Why in standard deviation for a sample we exclude 1 value? And why only 1, and not 2, or 3, or 1.5? This does not seem too inclusive and equalitarian. And why excluding and not including? Excluding will distort the result value making the standard deviation seem greater that it would be if used the population formula. But it seems very arbitrary that the compensation for using a sample instead of the whole population would only be 1 value and only excluded, not included.

Why the variance is 1 step behind of standard deviation? It could be considered as standard deviation squared, but the result would be the same. You correctly explained that standard deviation has the advantage of preserving the order of magnitute or the units. But what does variance mean? Preserving units means we can compare standard deviations measured for different samples, provided that the units, or more accurately, the thing we measure are really comparable. E.g. I can compare standard deviations of heights measured i USA and in UK. But does the variance allow for comparing, say, height and pay deviations? That would be cool and useful, but I guess squaring would not allow for it?

If all that was explained, then and only then the standard deviation (and variance) would be really simple. Right now it is still a formula with some elements of it seemingly randomly assembled that can be only mindlessly memorized but not understand. For me keeping things simple does not mean expressing it in a simple language with even the best visuals. That is only half the job. But you also need to justify that every piece of information is logical and can be deduced without having to memorize it mindlessly. Then if you forget the formula or its part, you would be able to reconstruct it in full.

[ajitandyokothakur]

There were two things you should mention in your tutorial:
1. Standard deviation is +/- because you are taking the square root of the variance.
2. You should explain why n-1 i.e. the concept of degrees of freedom. Since you calculate the mean from the sample, you lost one degree of freedom thus n-1, instead of n. For large sample size (30 or so), the difference between the two is minimal. Dr. Ajit Thakur (USA)