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.
Open paint. Get the curvy line tool. Draw a line. Make a lump that is perfectly center of that line.
“Skew” means that this lump is not perfectly center of this line. Left skew means it is more off to the left than perfectly center.
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