WEBVTT
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this question. Ask you to consider the pros and
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cons of using the mean as a description of central
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tendency. So we know that the mean is essentially
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adding up all of the data and dividing by how
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many data points there are, Um, we right
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, that is, that some of X over n
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equals X bar. So the mean is just the
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average of all the data points. What's what sort
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of the average? Well, there's a couple pros
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right away we know is pretty easy to calculate.
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Um, there are a lot of like calculators they
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confined online or even programming languages have built in functions
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to find means of big sets of numbers. It's
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ah, is a pretty easy method to find the
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center of ah, instead of data we know it's
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also it's pretty simple. There's only one thing we
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need to keep track of, um, and if
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we only have if we need one number to describe
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where the center of our data is thin, that's
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perfect. So it's easy and simple, and it
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really takes into consideration every single data point. Um
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unlike, say, for example, the median it
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doesn't take into consideration exactly where the other data points
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are. It only cares whether they're higher or lower
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than the median. Now, what are the cons
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? Well, one downside is that, uh,
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talking to describe a distribution with just the mean We
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don't know how spread out it is. We could
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have, um, a distribution that looks like this
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and a similar distribution that looks like this. And
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if they're centered on the same thing, the mean
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would have no way of telling apart those distributions.
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Um, so So even though this the central tendency
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is the same in each, the mean doesn't have
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a way of distinguishing these distributions. But it goes
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. It goes the same for the median. In
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other ways of of finding central tendency, the big
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one. The big downside of the mean, um
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is is when we have skewed distributions. That means
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if we have a distribution that's mostly centered over one
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bit, but has a couple of of data points
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that are way out toe one side instead of the
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mean being where the median would be, it's those
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points that are out to the side are gonna affect
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the mean a lot more than the points that are
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closer and so the mean will be drawn out into
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the wing of the distribution. This is a problem
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because now our median and are mean are different things
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. And we have no. They're two different descriptions
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of central tendency that are different, and so that
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discrepancy causes a little bit of trouble. And so
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that's a major drawback of just using the mean for
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central tendency. It's a good idea to have the
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median and the mean, or there's some other way
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of describing what this distribution looks like.