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## Summarizing center of distributions (central tendency)

Current time:0:00Total duration:3:55

## Video transcript

Find the mean, median,
and mode of the following sets of numbers. And they give us the
numbers right over here. So if someone just
says the mean, they're really
referring to what we typically, in everyday
language, call the average. Sometimes it's
called the arithmetic mean because you'll
learn that there's other ways of actually
calculating a mean. But it's really you just
sum up all the numbers and you divide by the
numbers there are. And so it's one way of
measuring the central tendency. The average, I
guess, we could say. So this is our mean. We want to average
23 plus 29-- or we're going to sum 23 plus 29 plus
20 plus 32 plus 23 plus 21 plus 33 plus 25, and then divide
that by the number of numbers. So we have 1, 2, 3,
4, 5, 6, 7, 8 numbers. So you want to divide that by 8. So let's figure out
what that actually is. Actually, I'll just get the
calculator out for this part. I could do it by hand, but
we'll save some time over here. So we have 23 plus 29 plus
20 plus 32 plus 23 plus 21 plus 33 plus 25. So the sum of all
the numbers is 206. And then we want
to divide 206 by 8. So if I say 206 divided
by 8 gets us 25.75. So the mean is equal to 25.75. So this is one way
to kind of measure the center, the
central tendency. Another way is with the median. And this is to pick out the
middle number, the median. And to figure out the
median, what we want to do is order these numbers
from least to greatest. So it looks like the
smallest number here is 20. Then, the next one is 21. There's no 22 here. Let's see, there's two 23's. 23 and a 23. So 23 and a 23. And no 24's. There's a 25. 25. There's no 26, 27, 28. There is a 29. 29. Then you have your 32. 32. And then you have your 33. 33. So what's the middle number
now that we've ordered it? So we have 1, 2, 3,
4, 5, 6, 7, 8 numbers. We already knew that. And so there's actually
going to be two middles. If you have an even
number, there's actually two numbers
that qualify for close to the middle. And to actually get the median,
we're going to average them. So 23 will be one of them. That, by itself,
can't be the median because there's
three less than it and there's four
greater than it. And 25 by itself
can't be the median because there's three larger
than it and four less than it. So what we do is we take the
mean of these two numbers and we pick that as the median. So if you take 23 plus 25
divided by 2, that's 48 over 2, which is equal to 24. So even though 24 isn't
one of these numbers, the median is 24. So this is the middle number. So once again, this
is one way of thinking about central tendency. If you wanted a number
that could somehow represent the middle. And I want to be clear,
there's no one way of doing it. This is one way of
measuring the middle. Let me put that in quotes. The middle. If you had to represent
this data with one number. And this is another way of
representing the middle. Then finally, we can
think about the mode. And the mode is
just the number that shows up the most
in this data set. And all of these numbers show
up once, except we have the 23, it shows up twice. And since because 23 shows up
the most, it shows up twice. Every other number shows
up once, 23 is our mode.