What is skewness? A detailed explanation (with moments!)

See all my videos at www.zstatistics.com/videos/
0:00 Introduction
4:28 Skewness calculation: Pearson
7:06 Skewness calculation: Moment-based
12:56 Skewness visualisation
14:02 Challenge question
For the moment video, see here:
www.zstatistics.com/descriptiv...
(will be up Feb 2019).
Series music by Purdy.
purdy.bandcamp.com/
Song: 3 Friends to the Stars

[@TheRollsP]

Negative Skew = Amount of efforts( e.g. in terms of time) put in studies from start of one semester to the next

[@eliebadlissi2818]

recalling the mode video graphic was hilarious. Excellent content as usual thank you!

[@user-iu5lj1oq2g]

I actually did a degree in Statistics very many years ago (knowledge which I have never used directly since) , and I would totally agree with your comments about hand-waving explanations about degrees of freedom from lecturers! Another that baffled me at the time was moments. Both your explanations were much better! Enjoying the videos as I try to remember what I learned (temporarily) at university.

[@bryantorres6057]

Distribution of age at death in a developed country.

[@judahdsouza9196]

perfect

[@amymjmurphy]

Your videos make all of this so understandable!! I am in graduate school and taking quantitative analysis, and this has helped me so much!

[@waeltoumi9650]

he is wrong in same examples

[@waeltoumi9650]

when the mean

[@ShiNguyenchu]

scenario for negative skew: a super easy close book test, so that the majority of the students get high mark while very few students get lower score

[@zedstatistics]

Good one! I've seen many of these. One has to question the integrity of these types of tests :)

[@prakharagrawal4011]

Same example if I see in my class but for Positive skew, As majority of student get low mark and few students get High score.

[@user-iu5lj1oq2g]

I thought about this before looking at the comments and had an idea very similar to yours, an easy exam with a few difficult questions given to a class where most people are pretty studious and a smaller number are lazy and/or stupid.

[@chaseezra5450]

instablaster

[@chunlangong2214]

define integrity

[@yoongwaichan6102]

Negative skewed data: Japan's aging population.

[@parthpardeshi1330]

Ya please explain

[@bryanross421]

@@parthpardeshi1330 It is simple... picture where the graph will be tailing off. It is going to be tailing off towards the left because Japan has an aging population and fewer people in the younger scale, hence negatively skewed. Also if you get an imaginary set of numbers where majority of the people are above 60, you will see that the mean is less than the median...try it

[@kshitijkumar6610]

Damn! Japan needs to work on this!

[@parthpardeshi1330]

@@bryanross421 Oh ya, that's easy, I wonder why I didn't get that 😅 Anyways thanks Bryan.

[@parthpardeshi1330]

@@kshitijkumar6610 How will that happen? Does the government need to promote a higher birth rate somehow?

[@kaykwanu]

You presentations are awesome....and intuitive. I will consume all your content!

[@shukailu6731]

Thank you Justin! Your video is amazing!! Cheers to all Math lovers here!

[@johnsonmshiu4837]

For example If you have provided an easy test to a students in a class majority of them will score high marks while few of them will score lower marks (Negative Skewness) and vice versa

[@XYZmmc]

The first video that could explained exactly true and all details, thanks

[@sundarramsrinivasan905]

The most commonly viewed parameter in a factory has negative skew. Machine speed. Another common one is impurities in a chemical process that build up over time and are purged periodically.

[@glorysonhorace3265]

I really can't thank you enough. May God bless you

[@laarydickman6147]

Awesome! The mode is central I thought it was the mean! Cleared things up for me. Thank you!

[@Poopy_Ass]

Joy Division reference was all i needed to be sold on this channel forever.

[@zedstatistics]

Ha! Had to re-watch to remember where I dropped it.

[@veronicanwabufo5905]

Thanks Justin. Your videos are interesting and I understand Statistics more. Do you have a good advanced stat textbook you can recommend, the one that talks about the applications of statistical concepts? Thank you

[@naftalibendavid]

Superb explanation. Loved the reference to Joy Division. Appreciate the commitment to accessibility with accuracy

[@zedstatistics]

Hehe a reference definitely lost on my younger students!

[@aneesasolwa9940]

the mode part was so extra. I loved it.

[@naftalibendavid]

Price of a book on the web usually has the new retail price as the mode on the far right and various discounted prices to the left at Lowe frequency...

[@avahsieh4645]

Negative skew distribution example: Wealth by age. As you grow older, usually you earn more.

[@abhinavshukla1264]

It think distributions are not something having an independent variable x ( like you mentioned age ) and there function f(x) ( like you say wealth.) It's different thing. In your case you choose x as age then the negative skewed distribution is representing that old aged people have greater probabilty of being there in a locale.

[@alecdelu83]

Not in Argentina

[@avahsieh4645]

@@alecdelu83 I am curious. What's it like in Argentina?

[@alecdelu83]

Government makes people pay every month a "percetnage for retirement" through taxes and then it steals it from their savings to pay the deficit they created in the first place, and to be even more corrupt. Result: destroyed country with poor old people.

[@avahsieh4645]

@@alecdelu83 Thanks for sharing your insight. Sorry to hear that your people have to endure this. Hope everything gets better and fairer in the future. All the best.

[@108987]

The outcome of writing put options with a strike price way below the current market price (out-of-the-money puts). Most of the time you will be making money (being on the righthand side of the distribution mass) but once in a while you will incur heavy losses (black swans) where the probability of occurring is low but severe (i.e in the left tail).

[@marzenazygis441]

Very well explained!

[@wyattsullivan2714]

Negative skew example: a measure of performance for a high level competition. For example, the javeline throw event in the Olympics.

[@barhammd]

Challenge: a high or low specification limit will indicate in a skewed data set, such as car speed data will be negatively skewed to the upper speed limit

[@vrindaarora7869]

Eg. Concentration in studies. First we struggle to get into that flow state , then when we actually get it our attention is high and then it falls again😂

[@goldfishdoc1999]

😂😂

[@farrukhzaidi3094]

Example of negatively skewed data: Submission of assignments by students. (if we take the date on x-axis and assignments submitted on the y-axis.)

[@pratibhasharma8457]

I love you and your classes... You are awesome

[@ruby_gleyzes]

Excelent video. Thanks!

[@esraaomer2227]

Thank you very much your explanation is very clear👏👏

[@arthigamyafinancialservice3793]

That recall video omg hilarious!

[@andreasengert4658]

Another example of negative skew: realized payoffs from loans to lenders. Most borrowers pay but some default.

[@mouradmadouni8277]

Thank you very much!

[@hrishikeshbhaumik307]

Examples of negative skew:- 1. Online reviews of a reliable product on a particular scale 2. Waiting time of customers at a popular eatery

[@astadash1598]

A negative skew can occur in a class of average students having an easy test to answer. In such a way most of students can have good grades and a few will have bad grades, as a result our data will be negatively skewed.

[@malharjajoo7393]

Negative skew: output of softmax layer in Neural networks. aka overconfident predictions

[@cahyaningsih5682]

negative skew: my heart

[@zedstatistics]

THIS

[@parthpardeshi1330]

How?

[@serenaS8406]

super helpful. Thanks

[@zhuwenhao4852]

great job.

[@richardpanduroallanson1076]

An anecdotal example of negative skew that reflects what some are already saying: I was on a science jeopardy team in high school, and we had weekly practice all semester for the end-of-semester science bowl. All the local high schools would compete in the science bowl. I never studied but attended weekly practices. When science bowl day came, everyone was constantly reading textbooks, including myself. My teacher told us he saw us study more on competition day than the whole semester combined... whoops. If time was on the x-axis, and the amount of studying was on the y-axis, my graph would be highly skewed... perhaps a skew = -2 or greater.

[@moguerestherg.6547]

Thank you very much.

[@user-ki3wu1gm6d]

Hello! Can you please explain building the L-moments ratio diagram for comparing best fit Probability Distribution Functions?

[@user-ri7xi7up8z]

Recently I did one project on Movie rating prediction where IMDB rating was right skewed and another scenario is human mortality rate.

[@AmitTiwari-wf1xj]

Negative skewness eg: Marks scored by student of 50 in Math in 11th class

[@michaelh.6308]

Perhaps for unpopular athletic events where many participants are approaching what is currently possible? Say, a high-jumping hobby club. A few members are new, but most of the members have stuck around for a while and are nearing the physical limits of jump height.

[@gregmakov2680]

negative skew is usually present in the statistics of grades in a class. Several students got bad grades, a handful amount of student got good grades, but just some of them have high grades.

[@felixgrant1]

Challenge: Anything with socially desirable responding. For instance, asking people how much healthy food they eat might mean that people want to appear healthy and so you end up with plenty of high values and few low values, resulting in negative skew

[@ranamaegulam3206]

This is our lesson in biostatistics, but I'm looking for a video that teaches how to explain negatively skewed or positively skewed data from a data set problem like E. coli levels in 50 beaches in a region. In highschool we are taught how to solve this, but now that I've reached college, we are more focused on explaining the answer to the solving. I hope you make a video about interpreting the results 🥲.

[@michaelh.6308]

I'm not sure why, but moments are reminding me a lot of derivatives. Are these related somehow? Position = x , change in x with time = velocity , change in velocity with time = acceleration. 0th, 1st, and 2nd derivatives. Position of average amount = mean, change in amount with distance from mean = variance, change in variance amount with distance from mean =skew 1st, 2nd, and 3rd moments.

[@Undercover_FE]

I know this is old, and I hope you are now well versed on these topics, but for anyone wondering: We are not finding deltas in moment calculations. They are just averages. Indeed, the first moment is the average of n elements, more so (since you mention physics) the Center of Mass of the n elements. That's why I don't agree with what is said in the video, that is when he states that we are finding the average distance from the origin for the mean calculation---this is not true since the negatives will always interfere in this calculation (Recall this is the entire motivation of the variance involving squares). The second (centralized) moment is the average area of squares each given by deviations from the mean. (xi - u) is the deviation from the mean, then squaring it, (xi - u)^2 , gives the area of that respective square. Do this for each i until reaching n, then add them all together, then dividing by n gives the average area. Square rooting the variance (the average area of squares, which we now arrange as a square) will give the length of the leg of said square holding the average area, therefore giving the average distance from the mean. Note that when using xbar rather than u, we have to apply Bessel's correction to move the variance estimate closer to the true variance (n-1). So, second moment is just an average area problem. Third moment is finding the average volume, BUT negative deviations yield negative on odd powers. So, if all negative volumes cancel with positive volumes in our centralized calculation, then we have a perfectly centered distribution. So, Mean: Finds center of mass Variance: Finds average area of squares each given by deviations from the mean Std Dev: finds length of leg of sqaure given by variance, which is therefore the avg distance from the mean Skew: averages centralized volumes then compares is to volume given by avg distance from the mean. Hence if the num > denom, we have large skew. We then apply correction for sampling. Also, Zed These videos are great. I have so many questions I would love to ask you!

[@chaineloisir2506]

I'm pretty sure if we check for the distribution of the debt in a population, using a negative number if you are a debtor and positive number if you are a creditor, it will result in negative skew.

[@amleshkanekar328]

Scenario for negative skew: The variable Age in a country which for an extended period of time, has had an excellent public healthcare system and also an enforced birth control policy such as a "one child policy".

[@wnualplaud2132]

And does the result from Pearson’s formula tell us anything about the relation of the spread between right and left compared to the mean. For example, the spread to the right is 2 times larger than the left?

[@surajpadhan8650]

Negative skewed : acquisition of knowledge (skill or experience) with time.

[@Spacetime23]

Please help me understand how the numerical formulae were derived for Skewness. I got the idea behind dividing the difference in Mean and Mode/Median by Standard Deviation for scaling purpose though !!...

[@walterreuther1779]

Negative skew looks like a hockeystick: Income, CO2, average temperature over time (these are not the typical subject of statistics I suppose) Another example could be all things associated with old age on the Y axis and old age on the X axis. (E.g. hearing loss vs. age, number of close people died vs. age etc.)

[@YRPortfolio]

Not sure, but perhaps temperature at which cells and viruses die. I vaguely remember proteins breaking down at around 42 Celsius

[@dr_ramy_abougreeda]

A classical example of Negative Skewed distribution is the distribution of the age of old people in a party with some of their children. 😊🎉

[@ckbyrd111]

Example of negative skew - Maillard browning in food as a function of temperature. At the molecular level, most food doesn't heat evenly, so some parts will reach the threshold temp and start browning early on, but relatively few. As the food temp exceeds ~140F, more of the surface will brown. If you keep raising the temperature, the amount of brown (as measured by light absorption/reflection) will flatten out, but never reverse (the food burns and carbonizes, which is still technically brown). See e.g. www.researchgate.net/publication/223019438_Temperature_effect_on_the_non-volatile_compounds_of_Maillard_reaction_products_derived_from_xylose-soybean_peptide_system_Further_insights_into_thermal_degradation_and_cross-linking

[@Shinykip]

Highly skewed data: income. Excellent video, by the way. Look forward to a follow up on kurtosis.

[@thumpinhippo]

@zedstatistics Thank You!! Great video. Can you help me understand what is a large or small sample in terms of when the mode is in/reliable?

[@thumpinhippo]

Un/reliable*

[@mendezcordero]

Thanks!

[@zedstatistics]

Thanks for the love, RM!

[@ankurkulshrestha1308]

Example of negative skew: currency coins. Majority of them will be from last few years, you may get a little very very old but you will never get for a future date.

[@KaeAlSa]

I have a real world negative skewed data set. A manufacturing production facilities throughout that isn't under control. They can only go so much over their standard rate before they hit their theoretical maximums. But they can miss it all the way down to 0.

[@JonhMalcovich]

Excelent!

[@rainjoyaman9470]

How do you draw the graph of skewness based on the value of skewness? I'm confused😩

[@faisaltasleemft]

an unequal distribution of income... the taxation body of underdeveloped countries and developing countries also show this type of distribution as most people pay the average or low-income tax, whereas only a few people pay very high-income taxes

[@rajeshnayak9199]

Student scores is one of the situation where we see the possibility of negative skewness.

[@rafaeljm3204]

Is Bragg Peak an example of left skewedness?

[@karankharayat193]

Negative skew - Selling Call and Put options. Profits are small and frequent in the form of premiums but the are small chances of a big loss.

[@luiscarlospallaresascanio2374]

Que programa usar para las presentaciones?

[@sukursukur3617]

Why do we calculate standard deviation by using mean? Namely, why dont we use mode instead of mean?

[@pesc75]

I'm working with a criterion reference evaluation. Most of our data for a sample or a population should be a negative skew distribution since we target a mastery result at more than 85% or so since it's criterion based evaluation. Am I correct?

[@cmrityun]

Another example of negetive skewness: Holidaying during the christmas time is more and slowly it slows down during the later part of the year.

[@sheshs8357]

An instance of negatively skewed distribution can be "utility of an amount of money "

[@ibrahimsiali2419]

Oh wow, I like that observation. Very perceptive of you.

[@skwasigr]

negativ skewness is also the distribution of arrival time in min of students before a lecture at a university

[@sidharthar567]

Negative skew scenario was my interview question for college admission

[@avi12]

0:01 When the "Skewness" blinks, the whole slide offsets by 1 pixel back and forth

[@paleozon]

I read somewhere that cricket scores are a good example of a negatively skewed distribution. Since I am completely ignorant of the game, I can only take the author for his word!

[@m.c.degroffdavis9885]

Data set with a negative skew: age at death in developed countries (y-axis) and number in population (x-axis); years of working in industry and salary (similarly, years of formal education and salary)

[@bryanstark324]

But why do we calculate the skewness and kurtosis values? How does that help us evaluate the data?

[@kahanbhalani3607]

Distribution of marks of students. There might be a some students who performed considerably bad and hence the date got negatively skewed.

[@adityabaksi636]

Dataset of the scores from an easy examination is an example of negatively skewed.

[@yunguzi1153]

negative skew: velocity samples in a flow

[@ricardoafonso7563]

. Thank you .

[@aritra4028]

Can you explain why we are dividing with Sigma cube?

[@shivrajbhatti1074]

what a rewarding video this is some educative shit

[@shantanubapat6937]

for most people their investment return when they trade on their own(as opposed to indexing) will be negatively skewed.

[@danielprager4723]

Negative skewed data: Heights (or weights) for an entire country, because young people that are shorter (or lighter) are a small proportion of the total population of the country; most of the data will be taller (or heavier)

[@satyajitdash3967]

Demand of Air Conditioners over the years or Demand of Sanitizer in year 2020

[@jeet1819]

Nice, Sir, Kindly shar the pdf as well.

[@cw9249]

why do we measure skewness? what are examples of uses?

[@sahibar]

retirement age of a population.. very few people retire early.. lets say before 40, majority of the population gets retired around 55-65.

[@ctRonIsaac]

While I am not positive, I think salaries of Undergraduates from a University would show a negative skew. We have fewer STEM students that other types of students, and their salaries are generally higher

[@ayushbhattacharya2894]

How about the price of items in a super high-end fashion store. Most items will be in the very high price range, and only a few items will have a low price resulting in a negative skew.

[@muznahraza3577]

Example for negative skew: Education and training expenses in the life of a person

[@sarathy319]

Can u tell why S.D is in denominator..coz it tells us that if S.D gets smaller , skew gets larger and that s confusing....

[@kingjohnkk]

not sure if anyone said this but a negative skew could describe population aging and death... more people die when they are older and such..

[@vinayshimpi3632]

Usually entrance exams(mostly MCQ based) have negative skew

[@davidlocke4977]

The notion of growth insists on an exponential curve, but game theory insists that exponential growth exceeds the game-theoretic value of the game. We see this in every boom/bust cycle.

[@maujmishra4098]

Price of things that rich people buy can be an example of negative skew

[@japhethchew1604]

negative skew- subscribers of zstats over time