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How to find a missing value given the mean | Data and statistics | 6th grade | Khan Academy - YouTube
Channel: Khan Academy
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- [Voiceover] Let's say you're
in the babysitting business
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and you like to keep a log
of whom you are babysitting.
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So in the last month
you babysat six children
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and you wrote the ages of
all six children in your log.
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But then when you go back
to your log you notice
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that some blue ink spilled
over one of the ages
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and you forgot how old that child is.
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And at first you're really worried,
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your whole system of
keeping records seems to...
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you know, you've lost information.
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But then you remember that every time
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you wrote down a new age that month,
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you recalculated the mean.
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And so you have the
mean here of being four,
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the mean age is four for the six children.
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So given that, given
that you know the mean,
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and that you know five
out of six of the ages,
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can you figure out what the sixth age is?
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And I encourage you to pause the video
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and try to figure it out on your own.
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So assuming you've had a shot at it.
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So let's just call this missing age,
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let's call that question mark.
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So let's just think about
how do we calculate,
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how would we calculate a mean
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if we knew what question mark is?
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Well, we would take the total.
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We would take the total of ages,
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of ages,
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we would then divide that
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by the number of children.
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We then divide that by the number
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of ages that we had,
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and then that would be equal to,
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that would be equal to the mean.
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Or another way to think about it,
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if you multiply both sides
times the number of ages,
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the number of ages on that side
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and the number of ages on that side,
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then this is gonna cancel with that,
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and we're gonna be left with the total
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The total is going to be equal to,
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is going to be equal to the mean
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times the number of ages.
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Mean times, and I'll just
write times the number,
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times number of data points,
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or number of ages.
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So maybe we can use this information,
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'cause we're just going to have this
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missing question mark here and
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we know the mean and we
know the number of ages.
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So we just have to solve
for the question mark.
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So let's do that.
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So let's go back to the beginning here,
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just so this makes
sense with some numbers.
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The total of ages, that's going to be
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five plus two
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plus question mark,
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plus question mark, plus two, this two,
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plus two plus four plus eight.
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We're gonna divide by the number of ages.
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We're gonna divide it
by the number of ages.
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Well we have six ages here.
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One, two, three, four, five, six.
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Six ages.
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And that's going to be equal to the mean.
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This is going to be equal to the mean.
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The mean here is four.
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So let's see, and this is just
how you calculate the mean.
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So let's see if we can simplify this.
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So five plus two is seven.
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Let me do this, that's the wrong color.
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Five plus two, five plus two is seven.
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Two plus four is six plus eight is 14.
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14.
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And then seven plus 14 is 21.
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So we're left with 21 plus question mark
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over six is equal to four.
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Now we can do what we did
when we just wrote it all out.
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We can multiply both sides
times the number of ages,
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the number of data points we have.
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So we can multiply both sides times six.
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We can multiply both sides,
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both sides times six.
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So six on that side, six on this side.
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Six in the numerator, six in
the denominator, those cancel.
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So all we're left is,
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on the left-hand side we're
left with 21 plus question mark.
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Alright. All of these other green numbers,
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those just simplified,
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five plus two plus two
plus four plus eight is 21
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and we still have the question mark.
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So we get 21 plus question mark,
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I want to do that green color,
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21 plus this question mark,
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the thing that we're trying to solve for.
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The missing number is
going to be equal to,
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is going to be equal to
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four times six.
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Well what's four times six?
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That's 24.
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And so what's the question mark?
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21 plus what is equal to 24?
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And we could, of course,
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you might just say, well
it's gonna be three.
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Or, if you want to, you could say well,
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question mark is going to be,
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question mark is going to be equal to,
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is going to be equal to 24 minus 21.
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Which is, of course, three.
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Which of course, so let
me just write this down,
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so the question mark is equal to three.
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So the missing age, you
were able to figure it out
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based on the information you had,
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because you had the mean,
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you were able to figure out
that behind this blotch,
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that behind this blotch you had a three.
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It's exciting.
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