Skewed Distributions and Mean, Median, and Mode (Measures of Central Tendency)
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- Опубликовано: 22 авг 2024
- Asymmetrical (Skewed) Distributions and Mean, Median, and Mode (Measures of Central Tendency). Discover the Relationship between the Mean, Median, and Mode for Skewed Distributions.
skewed distributions and mean, median, and mode
asymmetrical
skewed
central tendency and skew
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Video Transcript: Here let's take a look at positive and negatively skewed distributions and we'll also examine the relationship between the three measures of central tendency in each of those types of distributions. So our first distribution here is going to look something like this bear with the slight inaccuracies here due to the pin tablet. We have right here is one measure of central tendency, here's a second, and here's a third. They're about evenly spaced they could vary in practice but the key here is the ordering. OK this first one is notice how it's the highest point in the distribution here, right? So that is the mode. The mode is always the highest point in the distribution. OK then the next one. Actually let's skip over this one. If you think about the measures of central tendency, which one is most influenced by the outliers or the extreme scores over here? Which measure of central tendency in other words is pulled towards the tail of the distribution? Well, that is the mean. The mean is the one that is pulled towards the tail. So it's going to be the furthest to the right. And then that only leaves us with one more left, right? That would be the median. So the median is in the middle here. OK and this type of distribution, if we have a number line here this is the positive end, this is the negative end. So remember the skew is determined by where the tail goes. So the tail here goes to the positive end so this distribution is known as positively skewed or it has positive skew. Let's look at the other side here. Here we have the opposite type of distribution. Here's the negative end on a number line, here's the positive end. The tail here points to the negative end, so this is a negatively skewed distribution. OK the highest point is somewhere around here. So the highest point's there. So what's this one? That is the mode, that's I would say the easiest of the three to figure out. And then we have two more lines here; one here give or take, and then one here. Look at this one it's the closest to the tail and that means it's influenced by these extreme scores. So that would be the mean. And that leaves us with the one that's in the middle. That's a clue there. The middle one is the median. The median is the middle score. And in these two types of distributions it's going to be the middle measure of central tendency. Let's say that on our number line here, this was 10, this was 20, and this was 30. I'm just making these up but this point here is 10, this point here is 20, and this point here is 30. And then the same thing here: 10, 20, 30. OK so the 10 points to the mean, the 20 points to the median, and the 30 here points to the mode. OK so in a positively skewed distribution notice how the mean is larger than the median, which is larger than the mode. So you could say something like this: the mean is greater than median, which is greater than the mode. In a negatively skewed distribution it's the opposite: notice that the mode is the biggest at 30, followed by the median at 20, and then the mean 10. So here we have mode greater than median which is greater than the mean. OK, that's it. For positively skewed and negatively skewed distributions, this shows the relationship between the three measures of central tendency.
Channel Description: For step by step help with statistics, with a focus on SPSS. Both descriptive and inferential statistics covered. For descriptive statistics, topics covered include: mean, median, and mode in spss, standard deviation and variance in spss, bar charts in spss, histograms in spss, bivariate scatterplots in spss, stem and leaf plots in spss, frequency distribution tables in spss, creating labels in spss, sorting variables in spss, inserting variables in spss, inserting rows in spss, and modifying default options in spss. For inferential statistics, topics covered include: t tests in spss, anova in spss, correlation in spss, regression in spss, chi square in spss, and MANOVA in spss. New videos regularly posted. Videos series coming soon include: multiple regression in spss, factor analysis in spss, nonparametric tests in spss, multiple comparisons in spss, linear contrasts in spss, and many more. Subscribe today!
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Have to tell you, I have my Doctorate Degree in Clinical Psychology and I have NEVER understood this concept until now. You are truly brilliant! It is ridiculous how most teachers/professors basically baffle you with their brilliance and BS but do not know how to effectively teach. God speed to you Man! I wish you had been my teacher when I was in school!
Joe Walsh
Hi Joe,
Thanks for the kind words - I appreciate it! I'm glad to know that you found the video helpful. Please spread the word!
Ron @ QS
Wow! Finally a video that explains how the measures of central tendency work in positive and negatively skewed distributions! Thanks!
My psychology textbook didn't explain that "the skew is where the tail goes" so I had no idea why one graph was called a "positively skewed graph" and the other was called a "negatively skewed graph". This is why I love youtube because it EXPLAINS.
This is so simple!!! Yet, I was only able to learn it from you! :) Thanks for the help.
Thank you so much! i was stuck on this for past 3 weeks and you explained it in simple words
!! Thanks.
This is a perfect video!! So simply and accurately explained thank you sooo much!!
waoww well explained. thank you so much
+rose ross
My pleasure, Rose. Please spread the word!
The explanation was simple and clear. thank you Sir
finally i am able to understand this concept . thank uhhh so so much.
Thank you for this!!!!!!
So nice explanation. Thanks you sir.
Great explanation! Though I think there is an important missing piece: the comparison between the MEAN and the MEDIAN! It would be great if you explain why the median is between the mode and the mean. Is it always the case? What is a rigorous and an intuitive way to think about this comparison?
Yes the median will always be between the mode and mean in a skewed data set or skewed distribution. In his description of the positively skewed distribution, a few relatively high values or outliers are pulling the mean to the right and away from the mode. The median value is the value with 50% of the observations below it and 50% of the observations above it. Those outliers are spreading the last 50% of the values out further along the number line and pulling the median away from the mode, but not as much as they pull the mean away from the mode.
i am currently studying statistics and i came across your video. i have to say it really really helped me. Up until now i never understood anything about the mean mode and median and how distributions affect it! I just want to know though why is the mean pulled towards the outliers and why the median is between the mode and mean. Is it because it supposed to be in the middle? But the median isnt realy in the middle of the graph....
I agree with the comment below that your instruction is very clear. I would like to ask about standard deviation of a skewed distribution, from the point of view of high school level maths.
Taking your positively skewed distribution in the video, if we had a data set with the mean, median and mode as per the values in the video, but we also knew the standard deviation was 15 (say), does this tell us anything in a quantitative sense, other than "the 'average' deviation from the mean is about 15".
Also, whats a good way to get a quantitative feel for the relevance of the standard deviation in skewed data. Say, for example, a second data set that mimicked your positively skewed distribution (in terms of mean, median and mode) had a std dev of 18, what quantitative comparisons might be drawn between this data set, and the one I mention above (std dev = 15)? I.E. How can one get a feel for what a difference in std dev means, quantitatively. In other statistics areas, such as box plots, the relevance of the Q1, Q2 and Q3 values can be readily understood and visualised.
Well described!
Well explained. Thanks!
This is epic
You deserve a salute..
I'm very grateful for your help
Thank you this video was very clear and very helpful!
It's easy to understand. Thank you! 😊
Really Nice Explanation , Thanks
Excellent explaination
THANK YOU!
you just saved me. Thank you SO MUCH
+Grace Baek
That's great to hear, Grace! Thanks for posting!
Thank you for this video! A really great help! ❤
Thank you so much! It really helped 😊
Why do we calculate standard deviation by using mean? Namely, why dont we use mode instead of mean?
wow such a clear explanation thank you
Thank you this was really well explained. Very helpful ! :)
My pleasure, Melissa. Thanks for letting me know you found it helpful!
👌👌very Nice...easy to understand
my God thank you so much for this
Do outliers cause the data to be skewed?
+MC Phong La
They certainly can. If they tend to pile up on one end of the distribution, then this will be the case.
I was given two CDF graphs, indicating two tourists (male and female). Number of sample for male was 26 while for women were 25. I was told to match the figures with either this is for males and this is for females with three reasons. How to match them?
Hello, if I have a daily sales sample for 365 days, the mold is 0 units, and max is 8 units, medium is 0 units, mean is 0.18 units....Can I say this will be a positive skewed distribution? Thank you.
Thank you!
Thank u so much for yr explanation
My pleasure, Minn!
brilliant...
why two formula of pearson don't give same result? what does it mean?
Thank you ☺
Thank you!!
So how can we define it properly?
THANK U !
My pleasure - glad you found it helpful!
thank you :D
🕊
nice!
woow
Thank you!!!
Thank you!