Question

A population of scores has µ = 10 and σ = 2. If every score in the population is multiplied by 4, then what are the new values for the mean and standard deviation?

a. µ = 40 and σ = 2
b. µ = 10 and σ = 2
c. µ = 40 and σ = 8
d. µ = 10 and σ = 8

Answer 1

The new mean after multiplying by 4 is 40, and the new standard deviation is 8, making option c the correct answer.

Step-by-step explanation:

When every score in a population is multiplied by a constant, the mean (µ) and the standard deviation (σ) of the population are also affected by multiplication. The mean is directly multiplied by the constant, so in this case, the new mean is 4 × 10 = 40. On the other hand, the standard deviation is multiplied by the absolute value of the constant, resulting in a new standard deviation of 4 × 2 = 8. Therefore, the correct new values for the mean and standard deviation are µ = 40 and σ = 8, which is option c.