Sorry, in the example the standard deviation is of course 11.50 and not 12.06!!!! If you like, please find our e-Book here: datatab.net/statistics-book 😎
Never forget, the results of ANY calculation depends on the quality and quantity of the data. In regard to hate, it is impossible to measure, impossible to determine and impossible to calculate because hate cannot be quantized.
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.
Ma'am, you are awesome. The simplicity exeh! Usually people come to RU-vid 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!
I really want to thank you so much for your great videos and how you explain all concepts in a very clear, simple way. Thanks, please continue posting videos my dear German lady. Wish you all the best 🙏🙏
Thank you, but... something always bothered me with SD but I never dared/could ask. I see that we square the differences so that they don't cancel out each other but actually we wouldn't have to: summing the absolute values of the differences would work just as well. From other sources, I understood that squaring distorts, enlarges big differences from the average which is good but there's no explanation why. Why can't we examine the differences from the mean just the way they naturally are, by averaging their absolute values instead of squaring them and square rooting after summing? If I got some explanation for this, probably 30 yrs of mist in stats would disappear.
Me too. I know the "what" but they rarely explain the "why", i.e. why do we square things, why do we divide by n-1 (how does it help anything?), why we need both variance and standard deviation if both are so similar, etc. why?
One of the problems with taking the "absolute deviation", which is what you have described and is a possible means of looking at the deviation, is that it is not differentiable at zero. When you take the standard deviation, it results in a smooth curve. Another factor is that the standard deviation more closely represents the Gaussian distribution, which is one of the more common types of distributions due to the Central Limit Theorem. My hypothesis is that the absolute deviation would be better for a uniform distribution, but someone more knowledgeable should correct me if I am wrong.
The standard deviation method gives a useful insight into how much the data varies, more so than just summing the differences and dividing by the number of samples gives. Take this really simple example. 5 people with heights of 160 154 155 156 150cm The mean is 155cm If we simply take the average of the absolute difference from the mean we get 2.4cm This sounds fine at first, but look at the total range of the values, it's 10cm, so is 2.4cm a useful metric of the data? The standard deviation of the same data set is ~7.2cm, much more realistically representing the core set of data in the "range", as hinted at by @Flexpicker below. I'm not sold on how useful the "variance" is though! The squaring and then square rooting helps to make it into an easy formula and removes the negative values created by choosing which order to subtract the values in said formula. The same method is used to measure AC Voltage, the mean would always be zero, so we take the RMS (root of the mean of the squares) which gives a useful metric of any data set that includes both positive and negative values. Hope that helps someone.
Thank you! 1) You explained, which method (N vs N-1) I have to use in which situation. But I didn't understand, why. 2) when "standard deviation" means the "mean value of all deviations": why I have to square the differences?
Very well explained the Standard Deviation. But, you have explained the difference between SD and Variance only mathematically. Please explain the difference conceptually.
Hi : ) The standard deviation (SD) is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. Here’s how you can interpret the standard deviation: Consistency: Smaller values of standard deviation indicate more consistency in the data set, meaning the data points are closer to the mean. Spread of Data: Larger values suggest a greater spread around the mean, meaning the data points are more dispersed from the center. The standard deviation does not directly tell you whether to use the mean or the median as a measure of central tendency. However, it can provide indirect insights: Effect of Outliers and Skew: If the data is symmetrically distributed (i.e., not skewed), the mean and median will be similar, and using the mean is typically effective even if the data has a high standard deviation. However, if the data is skewed or contains outliers, the standard deviation might be large due to these factors. In such cases, the mean might be misleading because it is affected by extreme values, whereas the median might be a more robust measure as it is less sensitive to outliers and skewed data. Thus, while standard deviation itself doesn't dictate the choice between mean and median, it contributes to understanding the distribution's characteristics, which can guide the decision. Regards, Hannah
"standard deviation, is the average distance of all measured values of a variable from the mean" (minute 6:28) - are you sure? To me average distance from the mean is (18+8+15+8+9+6) / 6.
Hi : ) the practical difference between standard deviation (SD) and variance lies in their interpretation and usability. Variance, calculated as the average of the squared deviations from the mean, is useful in statistical computations but is less intuitive due to its squared units, making it difficult to directly understand the spread of data. Standard deviation, on the other hand, is the square root of variance and is expressed in the same units as the data. This makes it much easier to interpret and widely used in reporting and analyzing data variability, as it directly describes how spread out the data is around the mean. Regerds Hannah
Why not use the sum of absolute values of the differences between the mean height and the individual heights, and then divide that value by the number of individuals?
1:00 This calculation is the Average. Not the Mean (in my world). The Mean is a line that divides an equal number of samples above and below the line. The Average does not always get you that. The Mean is more meaningful than an Average because your outliers will not skew what represents the middle. The reason why the Mean is less often used is it is computationally more intensive because the data has to be sorted.
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.
@@claudiacuevasgomez285 brain rejected you when you went for a brain implant? **I** care and so do at least **4** other people who gave my comment a "thumb-up". Go troll someone else!
@@2k7Bertram i care. obviously... i don't care what you say, though... and it was meant as a constructive criticism, unlike you that just want to be seen... bye, troll!
OP wasn't rude, it's just a correction. It's important to be as clear as possible. She's speaking English, so pronouncing words in English is ideal. I was confused at first, but figured it out because of the graphics. But without the graphics, it would have been much more confusing.
As has been noted in the comments, the standard deviation you gave in your example is incorrect. It is 11.5, not 12.06. I thought my calculator was broken, for a minute. :-) Also, in general, the standard deviation isn't "the average of the deviations," as you stated. If that were the case, the standard deviation in your example would be: (18+8+15+8+9+6)/6=10.67. Generally, one standard deviation is an interval above and below the mean that captures about 68% of the data in a given data set. It is a measure of "scatter" in a set of data, as you stated, but your explanation and implementation of the formula are both wrong. You should update the video to fix the mistakes, or take the video down. As it is now, your video will confuse people and likely lead to lots of errors, which I'm sure is not your intention.
if you are majoring in any science or business field in an American university, you will be required to take a introductory Statistic course in your freshman year.
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.
@@jdoesmath2065 Thanks, but what exactly? I asked at least 3 questions, so it's rather difficult to match your answer. And if what you mean is taking the derivative, what does it have to do with anything? Why all of a suddent we need to take the derivative? I know it's fun, and for that reason we could as well do integration, but will it give us any practical information?
@@piotrrybka318 Sorry, I was referring to the question about the standard deviation and why we square the differences instead of using the absolute value. The squaring function is differentiable whereas the absolute value function is not. Behind the formulas we use in elementary statistics is a lot of calculus.
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
It is 10 grade subject in "Math for 10 class/year " Is under section "ungrrouped obsevations" chapter. There you start learning "Average function" and "Median function ", Boxplots, Outliers and next statistic is the "grouped observations" where you learn calculating the "hyppighed" ( the most meated observations on the set " and the "frequency" on the bar chart . ( y axis ) . There you already got a fundament for buliding the continous learning goal, if you are planing to make vertical learning and obtain a crazy certificate of math or datalogist.😈
Why should I square the difference? I’ve asked this question to all the teachers who taught me SD. Everyone has says, oh it’s there in the formula use it.
The differences are +ve and -ve. If we sum them up while calculating average value of differences, it will cancel out and not give a correct average. Hence using a math trick to retain them by squaring each value and making it all positive. This brings up another question, why not just take modules instead?
Nice and easily explained, but I have used two methods for calculating the standard deviation (the above being one of them), and both come to 11.50 and not 12.06.
😄You answered a question I've always had, but never looked into it. Why the heck do you square the deviations to find the mean and then take the root of that, which is not really the correct average? You said, "If the arithmetic mean would be used it would be zero everytime". Hadn't looked into that. Now this provokes a new question: Why then not just take the average of the absolute value of the deviations? That would prevent the always zero result.
Many thanks for the nice feedback!!! I have just learned that there is a name for the metric you mentioned, it is called average absolute deviation. en.wikipedia.org/wiki/Average_absolute_deviation However, it seems that the standard deviation has become more accepted! Maybe also because of the variance, if the variance occurs in an equation, it is easier to continue calculating with it, it is easy to form the derivative and so on. Regards Hannah
You said "hates" but I got that. You are correct if weight is pronounced as way-ate, then height should also be pronounced as hey-ate. This language issue has baffled us (Indians) too.
Isn't this video mixing up standard deviation and average deviation (2:06)? The standard deviation is 11.50 or 12.06 depending on the formula, however the average deviation is 10.67. Am I getting this wrong or is it a tiny confusion mistake in the video?
I thought you said 'hate" instead of height and spent the first minute of the example thinking, "that's......a weird thing to use in a data science example". Lol
