Variance, Standard Deviation, Coefficient of Variation
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- Опубликовано: 21 авг 2024
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The coefficient of variation, variance, and standard deviation are the most widely used measures of variability. We'll discuss each of these in turn, finishing off with the coefficient of variation.
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Variance measures the dispersion of a set of data points around their mean value. Population variance, denoted by sigma squared, is equal to the sum of squared differences between the observed values and the population mean, divided by the total number of observations.
Sample variance, on the other hand, is denoted by s squared and is equal to the sum of squared differences between observed sample values and the sample mean, divided by the number of sample observations minus 1.
While variance is a common measure of data dispersion, in most cases the figure you will obtain is pretty large and hard to compare as the unit of measurement is squared. The easy fix is to calculate its square root and obtain a statistic known as standard deviation. In most analyses you perform, standard deviation will be much more meaningful than variance.
Alright. The other measure we still have to introduce is the coefficient of variation. It is equal to the standard deviation, divided by the mean. Another name for the term is relative standard deviation. This is an easy way to remember its formula - it is simply the standard deviation relative to the mean. As you probably guessed, there is a population and sample formula once again.
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#Coefficient #Variation #Statistics
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I swear this is the only video making me understand it. I do not know why others do not use a simple drawing, like you, to teach it. Great.
You're very welcome!
Best video about variance on youtube, finally someone that used a real life example rather than just solving the equation, keep them coming!
After many years, I have finally understood these concepts. You're a great teacher
Brilliant and concise. Thank you
You are welcome!
The amount of work that must have went behind making this is quite amazing. This is how you truly run a business.
In probability theory and statistics, the coefficient of variation, also known as relative standard deviation, is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as a percentage, and is defined as the ratio of the standard deviation to the mean.
The coefficient of variation shows the extent of variability of data in a sample in relation to the mean of the population.
Is the data distribution/spread (std) and data variability (cv) the same?
The coefficient of variation (CV) is a statistical measure of the dispersion of data points in a data series around the mean.
The explanation of the logic behind the use of 1 degree of freedom in the sample variance formula *chef's kiss* 👌
You got to be a genius to be able to explain this so that I can understand. Thank you.
Very helpful! Thank you... Im Spaniard and I understand it better in English than other videos in Spanish so you did a great work.
Thank You for showing the beauty of coefficient of SD
The coefficient of variation is helpful when using the risk/reward ratio to select investments.
this explanation is how children need to be taught in schools....good job
Hello! can you answer this questions? I need help!
1. How are you going to use variance standard deviation in your professional work in the future? cite a scenarion in your explanation.
2. Explain how the principle of probability may use in psychology business/tourism management?
Just yesterday I watched your cloud computing video and then came across this one for the standard variation. Very easy to understand how it works and what it does from your tutorial. Thanks again for creating such a quality video on the topic.
Thank you!
I love STAT, but the concepts are not easy. I was seeing STAT in a foggy mirror, now you made the mirror clear to me. Really really great thanks and STAY BLESSED!!!!
This is the best video explaining this that I've found so far, very well explained!
Great video about Variance, Standard Deviation, Coefficient of Variation! I also checked the article - it's very insightful with lots of information, examples and images. Amazing work!
Thank you!
This is such a quality video!! Thank you so much for providing stats students everywhere the opportunity to learn this material in both an effective and efficient way! Not all heroes wear capes!!
quality? is it about the video format quality?
@@crazieprince9380 No
Crystal clear explanation
Thank you !
Superb Explanation! You Rock 365 Data Science
Thanks...you enlightened my day! 😍😀
I really loved the video! I´ve been looking for a nice explaination of what variance really means, as you normally just get the formula without concrete example... and you did it great!
Thank you very much!
Glad it was helpful!
Clear and easy to understand. 👍🏼
Best explanation ever👍👍👍
Thanks a lot 😊
Perfect! not too much, not dumbed-down. Thank you!
thank you so much, it was really helpful for me!,
with love from Afghanistan.
Very well explained and with samples to boot! Excellent channel my bro!
Glad you think so!
Nice tutorial!
Thank you!
The explanation is so wonderful .
This is the first stats video in which I understood something.
I really appreciate you for the efforts you took to explain in simplest way possible.
Best wishes for your career.👍
Omg. I finally understood the topic(crying)
Why "n-1" is used instead of "n" for sample vairiance??
The quantity n − 1 is often called the degrees of freedom associated with the variance estimate.
In the equation: since the
last value of x − ¯x is determined by the initial n − 1 of them, we say that these are n − 1 “pieces of information” that produce s^2.
If the sample size is large, n-1 is not much different from n.
If the sample size is equal to one, no variance is there to be calculated, right?
[Walpole Myers - Probability and statistics]
i was a bit confused between these three, you made is clear very precisely, thank you.
Thank you so much. The way you explained it is so easy to understand. Many thanks
Thank you! We are glad :)
Amazing and clear explanation Really thanks
Nice vid. StDev & CV also is useful for Ag risk management and stock forecasting. In Ag, we compute probability in measuring crop yield per acre disbursements from StDev from mean for % of time over or under mean. CV scales to mean. Population is a good example too. Thanks!
Good overview of the terms, very useful to stats students!
Thank you!
Thank you!!! shortly, clearly, understandably!!!!
Thank you so much for this video. Finally able to understand it. Really appreciate it!
Very useful video for traders as well. Keep up the great work!
Thank you!
Moreover, What is the main difference between variance and SD?
when we will count Variance and when we will count SD??
Variance is more of an extreme example because it amplifies the differences if there is any. Standard Deviation is more low key and more close to the deviation from the mean. I think variance is used as a more sensitive device when finding deviation from the mean compared to SD.
I think variance is more useful when comparing data that has a more far-reaching consequence if they don’t conform to the right amount and you want to minimise that as much as you can, it being more sensitive is very useful in this scenario. Standard Deviation would be more useful if you value accuracy more than anything else.
Excellent explanation!
Excellent way to teach statistics. impressed.
Thank you very much for this video! It helped me understand the intuition behind these three types of variation metrics!
I think people, back when variance and SD were made, either forgot that we can just take "absolute" if we want the result in same units or they might've realised that after discovering the formula for variance, but didn't wanted to ruin all their effort and hence added a square root on top of that formula. With this they didn't only bring back the result in same units but also made the formula look even more mathematical.
Finally, a video I finally understood. Thank You!
Great explanation! Please increase the font size on computer screen because it cannot be seen on mobile screen.
Excellent explanation.
This helped me find my answer, thank you.
Thank you for the video, keep them coming!!
Thank you!
The lower the ratio of the standard deviation to mean return, the better risk-return trade-off.
Landon Mcintosh can you name any other practical world application CV is used for apart from risk-return trade off?
Amazing animation. Helped me a lot!
That's wonderful! Thank you!
Why are we using specifically (n-1) only for calculating the sample variance? If data is concentrated around the mean, then using (n-1) will overestimate the variance right?
And why can't we use mod(x-mean)/n to calculate the standard deviation instead of 2nd degree (squaring)?
Very well explained
Great video. I think you would have nailed it more and more🤓😇 if you gave an example of Standard-Deviation in practice like the in the Bell Curve. That would have shown folks what SD is good at. Give you a percentage probability of how a random data will deviate from a sample/population. 》》》 Still a great video.
Ah dude I needed this channel in my life so bad... Thanks!
very good and i learned so much!!!
3:07 if squaring amplifies the result doesn't that mean it over bloats the differences ?... and if the solution to that problem is to look at the standard deviation, then what's the point/advantage of calculating the variance and then square rooting it to get the standard deviation instead of using the mean deviation.. for e.g.
if the data for a value is 10,20,30,40,50... the mean is 30 the variance would be 1000/5 which is 200 and the step deviation 10*(root 2) the mean deviation would be (20 + 10 + 0 + 10 +20)/5 which would be 12 while that of step deviation is 14.14, mathematically I know why both aren't equal ( a^2 + b^2 is not (a +b)^2) but they should both represent the same thing right ?
maybe it goes back to him saying that if we don't square the difference of observed data sets minus the mean, it won't show true distance because there are negatives. but then again we could have just used absolute values instead of squaring so I'm with you on not knowing why the formula is this way 😂
May God granted you more knowledge. Nice video.
Thank you for sharing. It is easy to get understood.
Really helpful thanks
Thanks for the video
Great video!
Superb 👍🏼👍🏼.
Thank you.
You showed us and we'll remember. Thank you. 🙂
Thanks a lot for this beautiful explanation ☺️.
Thank you, this video was so clear!!
Great work... ❤️
well discussed
Thank you, this was very clear.
Thank you, how informative!!
Thank you!
calming voice! tq
This is very informative . thank you
Does both variance and standard deviation tell the spread of the data ?
Great explanation, thank you so much!
Glad it was helpful!
Amazing video👍
Started my stats unit for university and now currently on my 10th week and i still have no idea what my 2nd week classes was about until this popped up. Thanks alot ❤️😤
Lool same here, what uni for you?
@@nickcabrera3087 Murdoch uni in perth
@@victorgan4318 I passed, hbu
@@nickcabrera3087 haha mine exams are not till 2 weeks from now, congrats tho!! 🥳 i'm hella nervous
@@victorgan4318 study study study bro, you will be okay, I was fucking shaking as well but I passed, as long as its introductory stats and not some crazy shit then you will be fine my friend (math is my worst subject for sure)
This is very helpful. Thank you!
You're very welcome!
Thanks a Lot
Thankyou
Thankyou .
Ummm.. why did he pose the question "is there only 11 restaurants in NY?" I thought the n=10. I get why he asked the question but why did he change the hypothetical from 10 sampled locations to 11?
And WHY add the complication of pesos? Of course the CV of both are the same. What the heck does exchange rates and two lists of prices add to grasping the concept of CV?
Is this just so he can have two data sets to compare? If that is the case he should have compared 10 locations in two different cities so the results would NOT have the same CV and thus the calculation would be informative instead of obvious.
Great!
So population variance is basically squared average distance from each point to the mean
This was an amazing video
Amazing!!!
thanks broda
great video.
An amazing video thank you so much it helped an incredible amount!
Thankyou sir
Sir, in machine learning to calculate the dataset: mean, std, and coefficient variation, do you use a sample or a population?
Thank you so much
if 80% of jop applicants are able to pass acomputer literacy test ,find the mean variance ,and stadared of the number of people who pass the examination in asanple of 150 applicent
Nice
#jigyasaeducation
But why -1 for sample
Best one
fantastic
Tnx