One of the chief distinctions we'll make between shapes of distributions is whether they are symmetric, skewed left, or skewed right.
A histogram of a skewed-right distribution will have a tail that stretches to the right, and of course a skewed-left distribution has a tail in the other direction.
Here's how to make a good guess as to whether a distribution will be skewed one way or the other: If there's a lower bound , but no upper bound, the distribution might be skewed right. (Why?) On the other hand, if there's an upper bound but no lowerbound, then it might be skewed left.
For example, the distribution of income is often skewed right.
There's a lower bound (0$ per year -- let's not take into account
debt) but there's no upper bound. (This is not to say that you can
make infinitely many dollars per year, but to say that there are no ceiling
caps on income.) So the great majority of people are clustered within
a fairly modest 0-100,000 per year range, and then there are a few millionaires,
billionaires, and Bill Gates off to the right.
Questions:
1) Is the median income in the US likely to be higher than, lower than,
or about the same as the average income?
2) Can you think of a variable that is likely to be right-skewed?
Left-skewed?