Question

Given the sample −4, −10, −16, 8, −12, add one more sample value that will make the mean equal to 3.

Answer 1

Answer: The value to add to the set is 52

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For a moment, ignore the extra value we'll add in later.

The given set of values add to -34.

Let x be the extra value we add in. It adds to the -34 to get -34+x, then we divide by 6 because the set {-4,-10,-16,8,-12,x} has 6 items.

So we get the mean (-34+x)/6

Set this equal to the mean we want (3) and solve for x

(-34+x)/6 = 3

-34+x = 6*3

-34+x = 18

x = 18+34

x = 52

The set {-4,-10,-16,8,-12,x} updates to {-4,-10,-16,8,-12,52} and this set has a mean of 3.