How do you find the value of a score with this given information?

Question

A population of N=8 scores has a mean of μ=16. After one is removed from the population, the new mean is found to be μ=15. What is the value of the score that was removed? (Hint: Compare the values of ∑Χ before and after the score was removed.)

Answer 1

Questions like this one can often be solved by simply writing down what you know in the form of equations.

A population of N=8 scores has a mean of μ=16.

If we let X₁ be the first score, X₂ the second, etc., then this means that

(X₁+X₂+X₃+X₄+X₅+X₆+X₇+X₈)/8 = 16

since we're just taking the average. Let's suppose that X₈ is the one removed. It will be more useful, as the hint says, to group up the other scores using summation notation, so let's write this as

(X₈ + ∑_i=1⁷ X_i)/8 = 16.

or more simply

X₈ + ∑_i=1⁷ X_i = 128

After one is removed from the population, the new mean is found to be μ=15

This is now just

(∑_i=1⁷ X_i)/7 = 15

or more simply

∑_i=1⁷ X_i = 105

If you treat that sum that appears in both of our equations like a variable, you can quickly solve for X₈.