Starting with the data values 70 and 100, add three data values to the sample so that the mean is 86, the median is 82, and the mode is 82. Please show all of your work.

Question

Starting with the data values 70 and 100, add three data values to the sample so that the mean is 86, the median is 82, and the mode is 82.  Please show all of your work.

lgbasallote · Answer

have you tried trial and error?

anonymous · Answer

yes it just confuses me a bit more

lgbasallote · Answer

actually....it's not much of "error"... you know the start is 70 and the last is 100...then there are three blanks in the middle

70 _ _ _ 100

right?

anonymous · Answer

yes

lgbasallote · Answer

then it says the median is 82...so what do you think should you do?

anonymous · Answer

theoretically, it should look something like 70+82+82+x+100/5= 66.8

lgbasallote · Answer

exactly

lgbasallote · Answer

except... it says the mean is 86 so it should be (72 + 82 + 82 + x + 100)/5 = 86

anonymous · Answer

ohh. So, then how do you find that x?

lgbasallote · Answer

that should be $$\frac{70 + 82 + 82 + x + 100}5 = 86$$

lgbasallote · Answer

to solve for x, you should multiply both sides by 5 first

anonymous · Answer

so have 5*86, which comes to 430, and I believe we can subtract the original 334 by 430, right?

lgbasallote · Answer

right

anonymous · Answer

awesome. That missing number would come to be 96. Thank you!

lgbasallote · Answer

right