In this video, we discuss the location of the mean, median, and mode in symmetric, right skewed (positively), and left skewed (negatively) distributions. This video is part of the content available for free at www.statsprofessor.com/
I was doing higher math than in my grade level so it was getting harder until I couldn't understand it anymore. I found this video and I was so thankful and I understand it better.
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Love the way everything was explained, especially the mean being described as the balancing point. That really puts a fine point these concepts. btw, What happens to the empirical rule and probabilities implied by the bell curve when there's skewness? How do read it then?
I can’t think of a real life distribution with that structure, but it’s possible to draw one up using a simulator. However, it would not be a classic left or right skewed distribution. In general, you would need a long skinny tail on the right side to separate the mean and median, but you would also need the most repeated value to be something greater than the median. That would probably require a cliff after the median to enable a steep drop off after. Perhaps the mean would be the same as the mode in that case. Either way, the main idea to remember is that in a asymmetric distribution, the mean will move to the side of the curve where the more extreme values are.
In a distribution, there may not be a mode (the uniform distribution for example). In the uniform distribution, the mean and median are the same because it is symmetric.