Question

For each of the following populations, would a score of X = 50 be considered a central score (near the middle of the distribution) or an extreme score (far out in the tail of the distribution)?

a. μ = 45 and σ = 10
b. μ= 45 and σ = - 2
c. μ = 90 and σ = 20
d. μ = 60 and σ = 20

Answer 1

A score of X = 50 is considered a central score for populations A and D, and an extreme score for populations B and C.

Step-by-step explanation:

In order to determine whether a score of X = 50 is considered a central or extreme score, we need to compare it to the population mean and standard deviation.

a. For population A with a mean (μ) of 45 and standard deviation (σ) of 10, a score of X = 50 would be considered a central score, as it falls within two standard deviations of the mean.

b. For population B with a mean (μ) of 45 and standard deviation (σ) of -2, a score of X = 50 would be considered an extreme score, as it falls outside the possible range of values.

c. For population C with a mean (μ) of 90 and standard deviation (σ) of 20, a score of X = 50 would be considered an extreme score, as it falls far below the mean.

d. For population D with a mean (μ) of 60 and standard deviation (σ) of 20, a score of X = 50 would be considered a central score, as it falls within one standard deviation of the mean.