Standard deviation measures:
Correct Answer
D) How widely observations spread around the mean
Why this is correct: Standard deviation is a statistical measure of dispersion, quantifying how much individual data points (e.g., sale prices) deviate from the mean (average). A low standard deviation indicates tight clustering. Why the other choices are wrong: "The percentage change from one period to the next" describes a rate of change, not dispersion. "The difference between the largest and smallest value" defines the range. "The number of observations in the sample" is the sample size. Exam tip: High standard deviation = unreliable average. Look for tight clusters in comparables.
Why This Is the Correct Answer
Standard deviation measures how widely observations spread around the mean, indicating whether a data set is homogeneous or dispersed.
Why the Other Options Are Wrong
Option A: The percentage change from one period to the next
Percentage change between periods is a growth rate, describing movement over time rather than dispersion.
Option B: The difference between the largest and smallest value
The difference between the largest and smallest value is the range, which uses only two observations.
Option C: The number of observations in the sample
The count of observations is the sample size, a separate figure from any measure of spread.
How Far From Average, Typically
How Far From Average, Typically. Small means the mean means something; large means it does not.
How to use: Report it alongside the mean. A mean without a dispersion measure hides how representative it is.
Exam Tip
Standard deviation describes the data; standard error describes the precision of an estimate drawn from it. Do not interchange them.
Common Mistakes to Avoid
- -Confusing standard deviation with standard error
- -Reporting a mean without a dispersion measure
- -Treating the range as equivalent
Concept Deep Dive
Analysis
Standard deviation measures dispersion β how far observations typically sit from the mean of their data set. A small standard deviation means the observations cluster tightly, indicating a homogeneous market where the mean is genuinely representative; a large one means they scatter widely, and the mean describes no particular property well. That distinction is what makes the statistic useful in appraisal: it tells the appraiser how much confidence a central measure deserves, and it is the raw material for the standard error, confidence intervals and any statement about how precisely a market value can be estimated from the data. It is expressed in the same units as the observations, so a standard deviation of $18,000 on sale prices is directly interpretable. The distractors name other things: a percentage change is a growth rate, the difference between extremes is the range, and the count of observations is the sample size.
Background Knowledge
Standard deviation measures dispersion around the mean in the same units as the data. It underlies the standard error and confidence intervals, and indicates how representative a central measure is.
Real-World Application
An appraiser reports a $248,000 mean with an $18,000 standard deviation, showing the market is tight enough for the mean to be meaningful.
More appraisal-statistical-methods Questions
A price index rises from 100 to 121 over two years. What compound annual rate does this represent?
A sample of four sales drawn from a market with 200 annual transactions is:
A set of comparable sales has a mean of $250,000 and a standard deviation of $20,000. What is the coefficient of variation?
A property sold for $400,000 and resold three years later for $463,050 with no physical change. What compound annual rate does this indicate?
An appraiser includes both 'total room count' and 'bedroom count' as independent variables in a regression model estimating single-family home sale prices. The variance inflation factor (VIF) for 'bedroom count' is calculated as 12.3. What is the most appropriate appraisal action based on this result?
An appraiser runs a regression of sale price on GLA, age, and a binary variable for 'renovated' (1 = yes, 0 = no). The estimated coefficient for 'renovated' is $18,400 with a standard error of $6,200 and a t-statistic of 2.97. Assuming a two-tailed test at Ξ± = 0.05 and 42 degrees of freedom, what conclusion is supported regarding the market's recognition of renovations?
To validate the functional form of a regression model used for adjustments, an appraiser plots residuals against predicted values and observes a clear inverted-U pattern. What does this pattern indicate, and what is the most defensible corrective action?
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What does it mean to validate a regression model?
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