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## Statistics and probability

### Unit 3: Lesson 1

Measuring center in quantitative data# Mean, median, & mode example

AP.STATS:

UNC‑1 (EU)

, UNC‑1.I (LO)

, UNC‑1.I.1 (EK)

, UNC‑1.I.2 (EK)

, UNC‑1.I.3 (EK)

CCSS.Math: , 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.

## Want to join the conversation?

- I have a question with regard to the mode (3:33):

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?(0 votes)- Both, because their are 2 twos and 2 fours.(3 votes)

- can ther be more than 1 mode(0 votes)
- well if we look at say 1,3,3,3,4,4,5,6,6,6,10,1,000 there are 3 3s and 3 6s so unless I overlooked a rule or something there can be more than one mode.

this message brought to you by HMaster & co.(1 vote)

- 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) - i dont under stand what it is asking it makes no sense can you make it more simple(4 votes)
- Mean = Average

Median = Middle, and if you have 2 numbers in the middle, find the mean of those 2 numbers

Mode = Most common number(0 votes)

- 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)
- 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)

- I always get so confused with the Median and Mean...

how to tell them apart?(2 votes)- Median basically translates to middle. And median wants you to find the middle number in a set of numbers. Mean is just the average, I've yet to find a way to remember that one. As long as you remember median looks similar to middle and mode is similar to most, you'll know the last one is mean(average).(1 vote)

- 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) - What if there are two modes?

EX: 1, 1, 2, 3, 3(2 votes)- so it is Bimodal ( the awnser is 1 and 3)(1 vote)

- How do you find mode when no numbers repeat(1 vote)
- 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)

- If I have 11, 12, 5, 3, x; mean 7.4 how to I find x?(1 vote)
- 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.