The title says it all, I have somehow graduated through uni not understanding what “left-skewed” or “negative skewed” really means. Thanks in advance!
In: Mathematics
>The title says it all, I have somehow graduated through uni not understanding what “left-skewed” or “negative skewed” really means. Thanks in advance!
Skewness is a property of the distributions of random variables, giving a measure of how the distribution varies asymmetrically about its mean value.
Imagine a bell curve (normal or Gaussian distribution). A perfect bell curve has a skewness of zero — its y-value is highest at its mean x-value.
In statistics, it is conventional to say a distribution’s graph is skewed “left” (negative) or “right” (positive) referring to the longer tail of a skewed distribution; this puts the y-value peak on *the opposite side* of the mean (e.g. a positive-skewed normal distribution will have the peak to the left of the mean, and a longer, thinner section on the right of the mean than a zero-skewed version).
Skew gets more complicated with different distributions and there are a few different ways to parametrize it, but this is the basic idea and most intuitive example I can think of.
EDIT: here is a more tangible example. Imagine you recorded the ages of several thousand people in a large city with a very high birth rate, low infant/child mortality, and poor end-of-life care (i.e. more babies are born and live to adulthood than some average, and fewer people live to very old age than some average). If you plotted these on a histogram, you would might expect to see the highest bars to the left of the mean age — that is, more young people — than to the right. This is a positive-skewed distribution.
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