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Mean, median, & mode example

AP.STATS:
UNC‑1 (EU)
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UNC‑1.I (LO)
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UNC‑1.I.1 (EK)
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UNC‑1.I.2 (EK)
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UNC‑1.I.3 (EK)
Here we give you a set of numbers and then ask you to find the mean, median, and mode. It's your first opportunity to practice with us! Created by Sal Khan and Monterey Institute for Technology and Education.

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  • primosaur ultimate style avatar for user De Metter Kenny
    I have a question with regard to the mode ():
    I can understand it if there is one number which appears most, but what if you have 2 numbers that appears as much?
    For example: 1,2,2,4,4,7,8
    What's the mode in this case?
    (1 vote)
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  • leafers sapling style avatar for user bereketnumber1
    can ther be more than 1 mode
    (0 votes)
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  • starky sapling style avatar for user Makenzie Ortega
    For the people that are having a hard time remembering the differences between these three here is what me and my class uses while were in class:
    Hey diddle diddle,
    The median is the middle
    You add and divide for the mean
    The mode is the one that appears the most
    And the range is the difference in between
    (3 votes)
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  • blobby green style avatar for user Ryan Williams
    i dont under stand what it is asking it makes no sense can you make it more simple
    (4 votes)
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  • purple pi pink style avatar for user Gargi Gupta
    I find it exceptionally weird that in the case of odd numbers, the median can turn out to be a number that isn't even a part of the data set.
    (1 vote)
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    • leaf green style avatar for user Shane McGookey
      This situation would only occur when you have an even number of observations, but you are correct; the median can be a number that is not in the data set.

      However, this is also true of the mean. It is very possible that when you calculate the arithmetic average of a data set that said number will not appear in the data set itself.

      Both the mean and median are meant to accomplish a simple goal: to better describe the data set. To accomplish that goal neither is restricted to the convention that they must appear in the data set.
      (3 votes)
  • marcimus pink style avatar for user Leanna :)
    I always get so confused with the Median and Mean...
    how to tell them apart?
    (2 votes)
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  • leafers seedling style avatar for user Gloria Latimer
    Do you learn this in this in 6th grade.I an homeschooled so I don't know.This is a lot to ask, but if you have time could you make a list of all the thing they do for public school math?

    Thank you for the videos!
    (2 votes)
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  • piceratops ultimate style avatar for user Cisco
    What if there are two modes?
    EX: 1, 1, 2, 3, 3
    (2 votes)
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  • male robot johnny style avatar for user christian.knight7214
    How do you find mode when no numbers repeat
    (1 vote)
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    • male robot johnny style avatar for user Thomas B
      If no numbers repeat (and there is more than one number) then most would consider the set to have no mode**. This would also be the case for something like { 2, 2, 2, 3, 3, 3, 8, 8, 8} where all numbers appear an equal number of times.

      ** I have seen some texts that would say all the numbers would be modes in this case, but that is not the typical definition.
      (3 votes)
  • leaf orange style avatar for user Paula Frazier Muffeny
    If I have 11, 12, 5, 3, x; mean 7.4 how to I find x?
    (1 vote)
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    • hopper cool style avatar for user Mr. Jones
      You will need to write and solve an equation using what you know about averages. Since you have 5 numbers, to find the average, you add them up and divide by 5. Just write this in mathematical language!

      (11 + 12 + 5 + 3 + x)/5 = 7.4

      Now solve this equation and you're done!
      (3 votes)

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.