Finding mean, median, and mode | Descriptive statistics | Probability and Statistics | Khan Academy


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.

100 thoughts on “Finding mean, median, and mode | Descriptive statistics | Probability and Statistics | Khan Academy

  1. there can never be 2 middle numbers… according to math antics if you have an even number of numbers and you need to find the middle then find the mode of the two closest numbers to the middle.

  2. What if in the mode all of your numbers shows up once. What will i choose?? The closest to the median???

  3. like this comment if you are here because you have a test tomorrow

  4. Man dude all of the other videos are confusing but dude that just made my life like 30x easier thank you so much

  5. this is so helpful. I wish i could be as bright as him……

  6. what if in the mode there are two number that are the top. What then?

  7. If there are too many numbers to list and I am given the Max and the Min numbers what do I do then

  8. Adam’s average on four test is 80. Which of the following CANNOT be the number of tests on which he earned exactly 80 points?
    (A) 1 (B) 2 (C) 3 (D) 4

    Hello Sir can you tell me the answer of the above question.

  9. I found this super useful I just wish you went over range too… 🙁 and 🙂

  10. You have written 24 as median but can we use 24.2 or 24.3?they also divide the whole set into two equal parts too.Hope to get an answer soon

  11. Helped a lot! I forgot how to do my hw and now I know (Why they teaching this late in 7th?

  12. In the sum above if their is a more than two same number then the mode is

  13. Really helpful man. Really wish my teacher was this good at explaining this.

  14. Wowww it's very easy… Thank u sir ur vedio is really very helpful for me..

  15. WHAT ABOUT IF YOU DONT HAVE A REPEAT NUMBER WICH ONE IS GOING TO BE A MODE???

  16. yaa correct when their is even but their is odd numbers who to consider to the median

  17. sir jab mode mei number repeat na ho tab kya formula use krege……. plz sir tell me

  18. You explained that better than my math teacher!! Who would dislike this video??!

  19. Amazing but for mode, what if 2 numbers appear the same amount of time? What will we do then!? If you get what I mean… For example: 2,23,45,67,23,87,92,67
    As you can see, 67 is repeated as well as 23, what should we do then? I hope that made it clearer. Please explain to me as I have a test soon! Thanks Khan Academy, u r amazing and you have helped me alot, could you help me for this too, this is also for the random person reading the comments. You have helped me alot through out the time ive been living (😂😅🤣) could you just help me for this too!? Thank you! Also, happy new year and i hope you had and amazing Christmas too!♡◇☆

  20. Thxs so much was in a math test and watched this on phone and u helped so much god blees

  21. Actually I'm here because of this.

    10,15,18,19,19,22,22,26,29,30 find the mode

    What's the correct answer? 19,19 or 22,22 or 19,19,22,22???

  22. Thx a lot bc I forgot my notes at school. Thx for always being there when I need u most Sal.

  23. A good way to think about arithmetic means is to think about the contribution that each element provides the total given that the weight of all elements is equal. Just wanted to throw this tip because is easier to understand arithmetic mean under this light.

  24. My teacher is letting us do a video of recording us Doing the following. Thank u for the help

  25. my math teacher made me watch this like if this is your problem to

  26. I'm relearning math to help my kids. I feel so dumb having to do this, but I was a troubled kid.

  27. there is another way of finding the mean
    add all the numbers then divide by how many numbers you've got
    eg: i have to work out the mean of 2, 3, 16 and 21. i add 2 + 3 + 16 + 21= 42. i have got 4 numbers (2, 3, 16, 21) so i divide 42 by 4 to get 10 remainder 2
    like the comment if this worked for u

  28. What if all the numbers appear the same time.
    AND YOU CAN’T FIGURE IT OUT
    AND YOU STILL DON’T UNDERSTAND
    AND CAN ONLY BE ONE ANSWER
    May the gods of math help.

  29. Thank you so much!! I have a math exam tomorrow! And i have no clue about these. Then after i watched this video i learned SOO MUCH! Thank you so much!!
    Who is here for the math Exam tomorrow?!??!

  30. math antics: is very bad, takes a long time to get to the point, many jokes nobody finds funny

    kahn academy: gets to the point and explains like no other with good jokes here and there

  31. My question is how would one find the mean, if not all given numerical values are present?

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