A population of N = 10 scores has a mean of µ = 6. After one score is removed, the mean is found to be M = 5. What is the value of the score that was removed?

To find the value of the score that was removed, follow these steps:

1. Calculate the total sum of the original population of scores.

   • The mean of the original population is µ = 6.
   • The number of scores in the original population is N = 10.
   • The total sum of the original population (ΣX) can be found using the formula: ΣX = µ * N.
   • ΣX = 6 * 10 = 60.

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

   • The mean of the remaining scores is M = 5.
   • The number of remaining scores is N - 1 = 10 - 1 = 9.
   • The total sum of the remaining scores (ΣX_remaining) can be found using the formula: ΣX_remaining = M * (N - 1).
   • ΣX_remaining = 5 * 9 = 45.

3. Determine the value of the score that was removed.

   • The score that was removed (X_removed) can be found by subtracting the total sum of the remaining scores from the total sum of the original population.
   • X_removed = ΣX - ΣX_remaining.
   • X_removed = 60 - 45 = 15.

Therefore, the value of the score that was removed is 15.