Question

an association of realtors reports state-by-state median existing-home prices for each quarter. why do you suppose they use the median instead of the mean? what might be the disadvantage of reporting the mean?

choose the correct answer below.

a. home prices are discrete data, and the median should always be reported instead of the mean for discrete data. reporting the mean would have the disadvantage of being more difficult to interpret.

b. home prices probably have a symmetric distribution which makes the median a better representation of the center than the mean. reporting the mean would give the impression that the \typical\ home price is much lower or higher than it actually is.

c. home prices are probably skewed to the left and not symmetric. this makes the median a better representation of the center than the mean which would be influenced by the extremely low priced homes. reporting the mean would give the impression that the \typical\ home price is lower than it is.

d. home prices are probably skewed to the right and not symmetric. this makes the median a better representation of the center than the mean which would be influenced by the extremely high priced homes. reporting the mean would give the impression that the \typical\ home price is higher than it is.

Explanation:

⚡ Using what you learned: comparing measures of center & spread

Step 1: Analyze the distribution of home prices

Home prices in a state or region are typically not symmetric. Instead, they are skewed to the right (positively skewed). This is because while there is a natural lower limit to home prices (they cannot be negative, and very few are extremely cheap), there is no upper limit. A small number of multi-million dollar luxury properties pull the distribution out to the right.

Step 2: Compare the effects of skewness on mean and median

• Mean: The mean (arithmetic average) is highly sensitive to extreme values (outliers). The presence of extremely high-priced homes pulls the mean upward, making it higher than what most typical families pay for a home.
• Median: The median is the middle value of the data set and is resistant to extreme outliers. It represents the price at which half of the homes cost more and half cost less, making it a more accurate representation of the "typical" home price in a skewed distribution.

Step 3: Evaluate the given options

• A: Incorrect. Home prices are continuous numerical data, not discrete, and the mean is not inherently harder to interpret than the median.
• B: Incorrect. Home prices are typically skewed, not symmetric.
• C: Incorrect. Home prices are skewed to the right (due to high-end luxury homes), not to the left.
• D: Correct. Home prices are skewed to the right. The median is a better measure of center because the mean is pulled upward by extremely high-priced homes, which would give a misleadingly high impression of the "typical" home price.

Answer:

D. Home prices are probably skewed to the right and not symmetric. This makes the median a better representation of the center than the mean which would be influenced by the extremely high priced homes. Reporting the mean would give the impression that the "typical" home price is higher than it is.