A sample of n = 8 scores has a mean of M = 10. After one score is removed from the sample, the mean for the remaining score is found to be M = 11. What was the score that was removed?

Sure, let's solve this step by step.

1. Determine the total sum of the original sample:

   • The mean of the original sample is $M = 10$.
   • The number of scores in the original sample is $n = 8$.
   • The total sum of the original sample can be calculated as: $\text{Total Sum} = M \times n = 10 \times 8 = 80$

2. Determine the total sum of the remaining scores after one score is removed:

   • The mean of the remaining scores is $M = 11$.
   • The number of remaining scores is $n - 1 = 8 - 1 = 7$.
   • The total sum of the remaining scores can be calculated as: $\text{Remaining Sum} = M \times (n - 1) = 11 \times 7 = 77$

3. Determine the score that was removed:

   • The score that was removed is the difference between the total sum of the original sample and the total sum of the remaining scores: $\text{Removed Score} = \text{Total Sum} - \text{Remaining Sum} = 80 - 77 = 3$

So, the score that was removed is $3$.