A population of N = 14 scores has a mean of μ = 34. After one new score is added, the new population has a mean of μ = 45. What is the value of the score that was added?

Answer 1

We do this one by working backwards. Recall that mean = sum of the numbers/(total number of numbers). We know the mean, and the number of numbers (scores) which are 34 and 14 respectively. Thus

34 = sum of the scores/14 multiply each side by 14 to get 34 * 14 = 476 which is the sum of the scores for the first 14 scores.

The new mean is 45 so we just need to determine the sum of the scores such that it returns 45 when we divide it by the total scores, which is now 15 since we added a single score.

45 = (value of the 15th score + 476)/15

45 * 15 = value of the 15th score + 476

675 = value of the 15th score + 476

675 - 476 = 199 = value of the 15th score