A sale-price histogram shows two apparent peaks. What is a reasonable next analytical interpretation?
Correct Answer
C) Investigate possible subgroups and sensitivity to grouping or sampling
Two visible peaks may suggest subgroups, but can also depend on binning, sample variability or other data structure. Investigate characteristics and repeat the graphical checks before defining market segments. A histogram alone does not prove recording error, sample inadequacy or a normal distribution. Distinct subgroup analysis requires evidence beyond the picture.
Why This Is the Correct Answer
Option C is correct because two apparent peaks may point to subgroups, such as different property types or locations, but they can also result from how the data were binned or from random sampling variation. Investigating property characteristics and repeating the graphical checks with different groupings tests whether the pattern is real before any market segments are defined.
Why the Other Options Are Wrong
Option A: A recording error has been proved by the second peak
Option A says the second peak proves a recording error. A histogram shape alone does not prove that any data were recorded incorrectly; the peak may reflect a genuine subgroup or a binning effect.
Option B: The data are too few to support any analysis of the shape
Option B says the data are too few to support any analysis of the shape. Nothing in the histogram by itself establishes that the sample is inadequate, and the sensible step is to investigate the pattern rather than dismiss all shape analysis.
Option D: Conclude the population is exactly normal and average the two peaks
Option D concludes the population is exactly normal and averages the two peaks. Two peaks are not evidence of a normal distribution, which has a single peak, and averaging the peaks could describe a price level where few sales actually occur.
Two peaks, look deeper
Think of two peaks as two questions: what kinds of properties sit under each peak, and does the second peak survive a change in bin width?
How to use: Use this when a question asks how to interpret an unusual histogram shape.
Exam Tip
Pick answers that call for investigation of a graphical pattern over answers that claim a histogram proves an error, normality or inadequacy.
Common Mistakes to Avoid
- -Treating a second peak as proof of a data error
- -Averaging two peaks as if the data were one normal group
- -Defining market segments from a histogram without checking property characteristics
Concept Deep Dive
Analysis
This question tests careful interpretation of a histogram with two peaks (a bimodal-looking shape). Two peaks can suggest distinct subgroups, but the shape can also depend on bin choices and sample variability. The reasonable response is to investigate before drawing a conclusion.
Background Knowledge
A histogram groups data into intervals (bins) to show the shape of a distribution. A two-peaked shape can signal that the data combine two different groups, but bin width, bin starting points and small samples can create or hide peaks. Confirming subgroups requires evidence beyond the picture, such as property characteristics.
Real-World Application
An appraiser charts sale prices in a market area and sees one cluster near older ranch homes and another near newer two-story homes. Before treating them as separate segments, the appraiser checks the property data and re-draws the histogram with different bin widths to see whether the two clusters persist.
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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