The asking price for homes on the real estate market in Baltimore has a mean value of $286,455 and a standard deviation of $11,200. The mean and standard deviation in asking price for homes in Denver are $188,468 and $8,230, respectively. Recently, one home sold in each city where the asking price for each home was $193,000. Assuming that both distributions are bell-shaped, which of the following statements is true?
A) The Baltimore home has the higher standard z-value.
B) The coefficient of variation for Denver is less than for Baltimore.
C) The Denver home has a higher standard z-value.
D) Both cities have the same coefficient of variation.

Question

Quizplus · Accepted Answer

The standard z-value is calculated by subtracting the mean from the observed value and then dividing by the standard deviation. For Baltimore: $Z = \frac{193,000 - 286,455}{11,200}$ results in a negative value, indicating the home sold for less than the mean. For Denver: $Z = \frac{193,000 - 188,468}{8,230}$ results in a positive value closer to zero, indicating the home sold closer to the mean but slightly above it. Since the Denver home's z-value is closer to the mean relative to the standard deviation than the Baltimore home's z-value, the Denver home has a higher (less negative or more positive) standard z-value.

The Asking Price for Homes on the Real Estate Market