A population has μ = 50.What value of σ would make X = 55 a central, representative score in the population?
A)σ = 1
B)σ = 5
C)σ = 10
D)cannot determine with the information given

Question

Quizplus · Accepted Answer

The central, representative score in a population is the mean, μ. Therefore, X = μ = 50. The standard deviation, σ, is a measure of how spread out the data is. A smaller σ means that the data is more clustered around the mean, while a larger σ means that the data is more spread out. In this case, we want X = 55 to be a central, representative score, which means that it should be close to the mean. Therefore, we want σ to be small. The smallest value of σ given in the choices is 10, so the correct answer is C.

A Population Has μ = 50