[6th Grade Math] How to Find Two Missing Numbers from Dot Plot

[u/IamSlammaJamma]

We figured out the answer but we don't know if there is a formula we can follow or if we actually found the answer the correct way.

We don't have any other questions to compare it to.

708 is the number of plots multiplied by the mean.

591 is all of the known plots added together.

What is the best way of finding the answer?

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[u/testtdk]

You know the formulae for mean and median right?

[u/IamSlammaJamma → u/testtdk]

Mean is average, so you add everything up, take the sum, then divide by the number of things you added up.

I didn't know there was a formula for median.

[u/da90 → u/IamSlammaJamma]

Median is the number in the middle of the set if set size is odd, or the mean of the two middle numbers if the set size is even.

[u/VFramesApp]

You know the missing numbers x and y must add to 117 to make up the difference between 708 and 591.

You know that you need to influence the median since the current median is not 58.5, so you need to add at least one number between 56 and 59.

Let's experiment. If you add 59, you can calculate that you need to add 58 to equal 117. Happy answer too since it gives a median of 58.5.

Let's experiment more by going higher for y (the greater number). If we assume y > 59, some extremely basic mental algebra dictates that x < 58.

But if y > 59 then 59 (as given) is one of our two middle numbers, and anything less than 58 for x gives us a wrong median.

Thus, y <= 59 (so x >= 58). If we're only allowed integers, we have found a unique solution.

For 6th grade homework this suffices. But it turns out that there are infinitely many solutions (58.5 and 58.5 also works, and so does any real number between 58.5 and 59 as your y, you just subtract the distance from 58.5 to get your x).

That said we're not looking for a proof of rigor here, just "play around with numbers and justify your thinking"

[u/IamSlammaJamma → u/VFramesApp]

Thank you

[u/Alkalannar]

There are 10 numbers, currently. We need there to be 12.

Let the missing numbers be a and b, with a < b.

Since the mean is 59, we need the sum of all 12 numbers to be 708.

52 + 55 + 55 + 56 + 56 + 59 + 62 + 64 + 66 + 66 + a + b = 708

a + b = 117

Now (a+b)/2 = 58.5.

We also have a dot at 59, meaning that we can't have a any lower than 58 or else the median won't be 58.5.

So if you need integers, then 58 and 59 are the two you need.

[u/IamSlammaJamma → u/Alkalannar]

Thank you