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
Using the same SD convention and measurement units, the larger SD indicates greater observed dispersion about the common mean. It does not determine observation count, collection period, individual property values or whether an estimated mean is reliable. Selection, sample size, distribution and applicability require separate assessment.
Why This Is the Correct Answer
Option A is correct because standard deviation, the square root of the variance, measures dispersion around the mean. When two data sets share the same mean and use the same SD convention and units, the one with the larger standard deviation has prices spread more widely around that mean.
Why the Other Options Are Wrong
Option B: Its properties are worth more than the other's
Option B says its properties are worth more than the other's. The two neighborhoods have the same mean price, and standard deviation measures spread, not level, so it does not show higher values.
Option C: Its sample contains more observations overall
Option C says its sample contains more observations overall. Standard deviation does not determine the number of observations; a small sample can have a large spread and a large sample a small one.
Option D: Its data was collected over a shorter period
Option D says its data was collected over a shorter period. Standard deviation says nothing about the collection period; time span would need separate review.
SD means spread
Standard deviation answers one question: how far do values typically sit from the mean. It describes spread, not size, count or timing.
How to use: Use this to eliminate choices that tie standard deviation to value level, sample size or time.
Exam Tip
If two groups share a mean, a difference in standard deviation is about dispersion only. Reject answers that read it as a difference in value, count or date range.
Common Mistakes to Avoid
- -Reading a larger standard deviation as higher property values
- -Assuming a larger standard deviation means a larger sample
- -Treating standard deviation as information about the time period of the data
Concept Deep Dive
Analysis
This question tests what standard deviation measures. With the same mean, a larger standard deviation means the observations are more widely dispersed around that mean. It does not reveal sample size, collection period or which properties are worth more.
Background Knowledge
Variance is the average squared deviation from the mean, and standard deviation is its square root, expressed in the same units as the data. A larger standard deviation indicates more variability among observations. Sample size, data selection, distribution shape and applicability require separate assessment.
Real-World Application
Two neighborhoods each show a mean sale price near the same figure. One contains a uniform tract of similar homes, while the other mixes small older homes with large new ones, producing a much larger standard deviation. The appraiser recognizes that the mean is less representative of a typical sale in the mixed neighborhood and looks more closely at comparable selection.
More Statistics Questions
Sale prices are $270,000, $290,000, $300,000, $310,000, $330,000. Treat the listed observations as the complete population and divide by n when computing the standard deviation. Report to the nearest dollar.
A sales sampling frame systematically excludes a relevant part of the target market. What is the principal risk?
An appraiser estimates a market-wide price trend using only sales data from one brokerage that specializes in luxury homes, without checking how other segments are represented. What is the principal concern?
Compared with analyzing one matched sale pair for one feature, what can a suitably specified multiple regression do?
The base-period median sale price is $400,000 and the current-period median is $460,000. Compute the price relative defined as current ÷ base, as a decimal to three places.
The assessment-to-sale ratios are 0.8, 0.85, 0.9, 0.92, 0.95, 0.98, 1.02, 1.05, 1.08, 1.1, 1.15, 1.2. Calculate COD as [average absolute deviation from the median ÷ median]×100. For even n, average the two middle ratios. Report the COD as a percentage to two decimals.
Assessment-to-sale ratios are 0.94, 0.96, 0.98, 1, 1.01. Compute the arithmetic mean. Report as a decimal ratio to three places.
Market data show a first quartile sale price of $405,000 and a third quartile sale price of $495,000. What is the interquartile range, to the nearest dollar?
Assessment-to-sale ratios are 0.96, 0.98, 0.99, 1.01. Compute the arithmetic mean. Report as a decimal ratio to three places.
Given first quartile $400,000, median $440,000 and third quartile $500,000, compute the trimean (Q1+2×median+Q3)/4. Report to the nearest dollar.
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For an independent sale-price sample, the sample standard deviation is $20,000 and n=16. Estimate the standard error of the mean as s/√n. Report to the nearest dollar.