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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?​

Question

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Solution

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: ΣX=μ×N=10×7=70 \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: ΣXnew=704=66 \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: Nnew=71=6 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: μnew=ΣXnewNnew=666=11 \mu_{\text{new}} = \frac{\Sigma X_{\text{new}}}{N_{\text{new}}} = \frac{66}{6} = 11

Therefore, the value for the new mean is 11.

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