Can someone please explain to me in relatively accessible language what is meant by "moment" in statistics? I haven't been able to find a satisfactory explanation anywhere, aside from thickly worded definitions or ambiguous examples such as, "The first moment is the mean."
Someone please tell me in plain English what moments are.
Many thanks in advance!
Someone please tell me in plain English what moments are.
Many thanks in advance!
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It looks a little different for discrete random variables where you have a only certain values, usually a finite number, than for a continuous random. In the discrete case, you add up a sum. In the continuous case you need to integrate.
You can have a raw moment, or a moment about some value, usually the mean in statistics.
Let's start with the first raw moment. You add up or integrate x p(x), where p(x) is the probability associated with the value x. What you get is simply the mean.
Next, let's look at the second moment about the mean. "Second" means you are going to square the term. "About the mean," where m is average, means that you are going to look at (x - m)^2. So you look at the sum or integral of (x-m)^2 p(x). That gives you the variance. As you can see it's a measure of the spread of the data around the mean. Moments about the mean are called "central moments."
The nth moment about a point c would simply be the sum or integral of (x-c)^n p(x). See http://en.wikipedia.org/wiki/Moment_%28m…
for more info if you want it.
You can have a raw moment, or a moment about some value, usually the mean in statistics.
Let's start with the first raw moment. You add up or integrate x p(x), where p(x) is the probability associated with the value x. What you get is simply the mean.
Next, let's look at the second moment about the mean. "Second" means you are going to square the term. "About the mean," where m is average, means that you are going to look at (x - m)^2. So you look at the sum or integral of (x-m)^2 p(x). That gives you the variance. As you can see it's a measure of the spread of the data around the mean. Moments about the mean are called "central moments."
The nth moment about a point c would simply be the sum or integral of (x-c)^n p(x). See http://en.wikipedia.org/wiki/Moment_%28m…
for more info if you want it.
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a measure of the shape of a set of points