A population of N = 7 scores has a mean of µ = 10. If one score with a value of X = 4 is removed from the population, what is the value for the new mean?​

To find the new mean after removing one score from the population, follow these steps:

1. Calculate the total sum of the original population.

   • The mean (µ) of the original population is 10.
   • The number of scores (N) in the original population is 7.
   • Therefore, the total sum (ΣX) of the original population is: $\Sigma X = \mu \times N = 10 \times 7 = 70$

2. Subtract the value of the score being removed from the total sum.

   • The score being removed (X) is 4.
   • The new total sum after removing the score is: $\Sigma X_{\text{new}} = 70 - 4 = 66$

3. Calculate the new number of scores in the population.

   • The original number of scores (N) was 7.
   • After removing one score, the new number of scores (N_{\text{new}}) is: $N_{\text{new}} = 7 - 1 = 6$

4. Calculate the new mean (µ_{\text{new}}) of the population.

   • The new mean is the new total sum divided by the new number of scores: $\mu_{\text{new}} = \frac{\Sigma X_{\text{new}}}{N_{\text{new}}} = \frac{66}{6} = 11$

Therefore, the value for the new mean is 11.