Two neighborhoods have the same mean sale price, but one has a much larger standard deviation. What does that indicate?
Correct Answer
A) Its prices are spread more widely around the mean
Why this is correct: The original explanation states that standard deviation measures dispersion. A larger standard deviation for the same mean indicates that sale prices are more spread out (i.e., have greater variability) around that common average. Why the other choices are wrong: Its properties are worth more than the other's is false because the mean is the same, indicating similar average value. Its sample contains more observations overall is not indicated by standard deviation; sample size is separate. Its data was collected over a shorter period is a possible real-world reason for higher dispersion, but the statistic itself only indicates the spread, not the collection period. Exam tip: Same mean + larger standard deviation = more heterogeneous market. The mean is a less reliable typical value in such a market.
Why This Is the Correct Answer
Why this is correct: The original explanation states that standard deviation measures dispersion. A larger standard deviation for the same mean indicates that sale prices are more spread out (i.e., have greater variability) around that common average. Why the other choices are wrong: Its properties are worth more than the other's is false because the mean is the same, indicating similar average value. Its sample contains more observations overall is not indicated by standard deviation; sample size is separate. Its data was collected over a shorter period is a possible real-world reason for higher dispersion, but the statistic itself only indicates the spread, not the collection period. Exam tip: Same mean + larger standard deviation = more heterogeneous market. The mean is a less reliable typical value in such a market.
More Statistics Questions
A set of comparable sales has a mean of $250,000 and a standard deviation of $20,000. What is the coefficient of variation?
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