Skew Chirality

Hello!

I think I might be facing a fundamental misunderstanding when it comes to right vs left-skewed distributions.
Currently, I am working through the Mastering Stats w/ Python and this is one of the quiz questions I am having a hard time with:

In what sense is this distribution right skewed? To me, it seems that the majority of the data is toward the left of the histogram.
Also, is it that the mean is less than the median in this case because the majority of the data, the count that is, takes on lower values?

Thanks in advance!

I recall learning positive and negative skew rather than right and left but focus on how the tail behaves (not the peak) as that’s the bit you’re concerned about. If it helps perhaps “slanted” to the right reads better than “skewed” to the right though the meaning is much the same. As for the mean consider a dataset like (0, 1, 1, 1, 1, 1, 2,) then add a single outlying value at 24. What happens to mean and median then? Would you still call that a majority?

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Thank you for providing the synonymous slant vs skewed - I think I am seeing more clearly now why the use of the word for such situations. Because, if we are to start with a symmetric bell-shaped distribution, it would be the tail that is almost being stretched in a way. Why are we more concerned with the tail vs the peak, though?

Regarding the mean, given your example, the outlier 24 would cause the mean to then become greater but would not dramatically change the median. So is it more a factor of outliers than where the majority of the data fall when determining if the mean is greater than the median and vice versa?

I don’t know that we’re more concerned with the tail than the peak. At a guess I suppose the peak will move very little which makes it a little harder to track and a weaker descriptor; if there’s a better reason then I don’t know it :laughing:.

That’s how I’d see it, you don’t need many values (not a “majority”?) to fall on one side or the other to affect the mean by a greater degree. At the end of the day you’re describing slightly different things with those two values. I suppose it depends a little on what you call a “majority” when you have a an asymmetric distribution.

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Great! Thanks for the insight!

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