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# Missing value given the mean

AP.STATS:
UNC‑1 (EU)
,
UNC‑1.I (LO)
,
UNC‑1.I.2 (EK)
CCSS.Math:

## Video transcript

let's say you're in the babysitting business and you like to keep a log of whom you are babysitting so in the last month you babysat six children and you wrote the ages of all six children in your log but then when you go back to your log you notice that some blue ink spilled over one of the ages and you forgot how old that child is and at first you're really worried your your whole log sister your whole system of keeping records seems to you know you've lost information but then you remember that every time you wrote down a new age that month Yury calculated the mean and so you have the mean here of being for the mean age is four for the six children so given that given that you know the mean and then you know five out of six of the ages can you figure out what the sixth age is and I encourage you to pause the video and try to figure it out on your own so I'm assuming you've had a shot at it so let's just call this missing age let's call that question mark so let's just think about how do we calculate how would we calculate a mean if we knew what question mark is well we would take the total we would take the total of ages of Ages we would then divide that by the number of children we then divide that by the number of ages that we had and then that would be equal to that would be equal to the mean or another way to think about it if you multiply both sides times the number of ages the number of ages on that side and the number of Ages on that side then this is going to cancel with that and we're going to be left with the total the total is going to be equal to is going to be equal to the mean times the number of Ages mean times and I'll just write times the number times number of data points or number of Ages so maybe we can use this information because we're just going to have this missing question mark here and we know the mean and we know the number of Ages so we just have to solve for the mark so let's do that so let's go back to the beginning here just so that this makes sense with some numbers the total of Ages that's going to be 5 plus 2 plus question mark plus question mark plus 2 this 2 plus 2 plus 4 plus 8 we're going to divide by the number of ages we're going to divide it by the number of ages well we have six ages here one two three four five six six ages and that's going to be equal to the mean this is going to be equal to the mean the mean here is four so let's see and this is just how you calculate the mean so let's see how we if we can simplify this so five plus two is seven let me just it that's the wrong color 5 plus 2 5 plus 2 is 7 2 plus 4 is 6 plus 8 is 14 14 and then 7 plus 14 is 21 so we're left with 21 plus question mark over 6 is equal to 4 now we can do what we did when we just wrote it all out we can multiply both sides times the number of ages the number of data points we have so we can multiply both sides times 6 multiply both sides both sides times 6 so 6 on that side 6 on this side 6 in the numerator 6 in the denominator those cancel so all we're left is on the left hand side we're left with 21 plus question mark all right all of these all these other green numbers those just simplify plus 2 plus 2 plus 4 plus 8 is 21 and we still have the question mark so we get 21 plus question mark I went into that green color 21 plus this question mark the thing that we're trying to solve for the missing number is going to be equal to is going to be equal to 4 times 6 what's 4 times 6 that's 24 and so what's the question mark 21 plus what is equal to 24 we could of course you might just know so well that's going to be 3 or if you want to you can say what question mark is going to be question mark is going to be equal to is going to be equal to 24 minus 21 which is of course 3 which of course so let me just write this down so the question mark is equal to 3 so the missing age you were able to figure it out based on the information you had because you had the mean you were able to figure out that behind the splotch that behind the sploshed you had a 3 it's exciting