A histogram of neighborhood sale prices shows two distinct peaks. What does this most likely mean?
Correct Answer
C) Two different market segments are present
Why this is correct: A histogram with two distinct peaks (bimodal distribution) strongly suggests the data set combines two different populations or market segments with different central tendencies, such as different property types, sizes, or quality levels within the same neighborhood. Why the other choices are wrong: While a recording error could cause an outlier, it wouldn't typically create two distinct peaks. A small sample size might make the shape unclear but wouldn't cause bimodality. A normal distribution produces a single, bell-shaped peak, not two. Exam tip: Bimodal data often means you are mixing apples and oranges. Separate the data into homogeneous groups before analysis.
Why This Is the Correct Answer
Two distinct peaks most likely indicate two market segments pooled in one data set, which is the standard interpretation of bimodality. The finding tells the appraiser to segment before computing anything, because summary statistics across mixed populations are misleading. It also points toward identifying what distinguishes the two groups, which is usually a visible property characteristic. Once segmented, each group can be analyzed on its own terms and the subject placed in the correct one.
Why the Other Options Are Wrong
Option A: The data contains a recording error somewhere
A recording error typically produces an isolated outlier far from the body of the data rather than a second organized cluster with its own peak. It would take a large number of coordinated errors to manufacture a mode. The shape described is systematic, not anomalous.
Option B: The sample size is too small to be analyzed
A small sample produces a ragged, noisy histogram where no clear shape emerges, not two clean peaks. If anything, bimodality is easier to see and more trustworthy in larger samples. Small size affects clarity rather than creating structure.
Option D: Prices are normally distributed in the market
A normal distribution is unimodal and symmetric, producing a single bell-shaped peak. Two peaks is the visual opposite of normality. The option would also imply that standard inferential procedures apply, which bimodality specifically undermines.
Two Peaks, Two Markets
One hump means one population. Two humps means you stacked two markets in one chart. Find what separates them, split the data, and analyze the half your subject belongs to.
How to use: When a stem describes distribution shape, translate shape into a statement about the population. Bimodal means mixed populations; skewed means outliers pulling one tail; symmetric single peak means one homogeneous group.
Exam Tip
In a skewed or bimodal distribution the median is a more informative measure than the mean, because the mean is dragged toward the tail or into the valley between peaks.
Common Mistakes to Avoid
- -Computing a mean or median across a bimodal data set
- -Deriving a market conditions rate from blended segments
- -Treating an unusual histogram shape as a data error rather than a finding
Concept Deep Dive
Analysis
A histogram displays how observations distribute across value ranges, and its shape carries diagnostic information before any statistic is computed. A single central peak tapering symmetrically in both directions suggests one reasonably homogeneous population. Two distinct peaks, a bimodal distribution, indicate that the data set is a blend of two populations with different central tendencies stacked into one chart. In a neighborhood price histogram the usual explanation is market segmentation: two product types such as townhouses and detached homes, two size or quality tiers, two eras of construction, or a waterfront and interior split within the same subdivision. That finding matters enormously to the appraiser, because measures of central tendency computed across a bimodal distribution describe neither group. The mean may fall in the valley between the peaks where almost no properties exist, and a market conditions rate derived from the blended data will reflect a shifting mix as much as genuine appreciation. The remedy is segmentation, splitting the data into homogeneous groups and analyzing the subject's group.
Background Knowledge
You need to read distribution shape from a histogram, including unimodal, bimodal, symmetric, and skewed forms, and the measures of central tendency and how skew separates mean from median. You should also know the concept of market segmentation and that comparables and trend data should come from the subject's own segment.
Real-World Application
An appraiser plotting neighborhood sale prices sees two clear peaks and discovers the subdivision contains both original 1,400-square-foot ranches and a newer section of 2,800-square-foot two-stories. She analyzes only the section containing the subject and explains the segmentation in her market discussion.
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?
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?
What does it mean to validate a regression model?
In a market study, what does a frequency distribution of sale prices show?
An appraiser includes months elapsed since each sale as a variable in a price model. What is this intended to capture?
An appraiser presents a statistical analysis in a report. What must accompany it for the reader to weigh it?
An R-squared of 0.86 in a sales model indicates that:
Which measure would best summarize the most common lot size in a subdivision?
Paired sales analysis and regression differ mainly in that regression:
Price per square foot declines as homes get larger. What does this imply for a linear regression of price on area?
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