Mean, median, & mode example

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 an 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 or you know the average I guess we could say so this is our mean we want to average 23 plus 29 over to some 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 have one two three four five six seven eight numbers so you want to divide that by eight 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 let's save some time over here so we have 23 plus 29 plus 20 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 point seven five so the mean is equal to 25 point seven five 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 20 then the next one is 21 21 then we go there's no 22 here there's let's see there's two 23 is 23 and a 23 so 23 and a 23 and no 24s there is a 25 twenty-five 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 one two three four five six seven eight numbers we already knew that and so there's actually going to be two middles if you have two if you have an even number there's actually two numbers that kind of qualify for the close to the middle and to actually get the median we're going to average them so twenty-three 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 or 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 two 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 in the middle and I'm gonna be clear there's no one way of doing it this is one way of measuring the middle 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 so 20 since because 23 shows up the most it shows up twice every other number only shows up once 23 23 is our mode