Given that: The average of a list of 4 numbers is 88.0. A new list of 4 numbers has the same first three numbers as the original list, but the fourth number in the original list is 82, and the fourth number in the new list is 96. What is the average of this new list of numbers?
To start, I tried arranging the data to see if that would make solving this problem clear.
I have Original: x,y,z,82=88.0 New: x,y,z,96=88.0
That is where it gets confusing for me because I don't understand how I find the missing values with just the average and one value.
I know that to find the average of the new list of numbers I must find the values of X, Y, and Z but that's what I'm having trouble with.
I'm aware that, to find the average we have to add the numbers, then divide the answer by how many numbers it is, but I am still very confused.
The answer choices are: A. 90 B. 91.5 C. 92 D. 92.5 E. 93.5
I've tried plugging in the answer choices as well, but it won't help, because I still need to find the values of X, Y, and Z.
The actual individual value of the first 3 numbers is unimportant, what is important is their sum.
We know $\frac {x + y + z+ 82} 4=88$, or $4\cdot 88-82=x+y+z$
Now we just want to know the average of $x,y,z, 96$, so take the sum you computed before, add to 96, and divide by 4.
There's easier ways to do the problem if you recall that each number contributes 1/4th of its weight to the average.