Sale prices are $200,000, $220,000, $240,000. Treat these as a sample and divide the squared-deviation sum by n−1 when computing the standard deviation. Report to the nearest dollar.
Correct Answer
B) $20,000
Mean=$220,000; Σ(x−mean)²=800000000. Standard deviation=√[800000000/2]=20000, rounded to $20,000. Variance and the data range are different quantities.
Why This Is the Correct Answer
Option B is correct because the mean is $220,000, the deviations are −20,000, 0 and +20,000, and their squares sum to 800,000,000. Dividing by n − 1 = 2 gives a variance of 400,000,000, and the square root is $20,000.
Why the Other Options Are Wrong
Option A: $16,330
Option A, $16,330, is the population standard deviation, which divides by n = 3 instead of n − 1: √(800,000,000 / 3) = √266,666,667 ≈ $16,330. The question asks for the sample version, √(800,000,000 / 2) = $20,000.
Option C: $40,000
Option C, $40,000, is the range, $240,000 − $200,000. The sample standard deviation is √(800,000,000 / 2) = $20,000.
Option D: $220,000
Option D, $220,000, is the mean of the three prices, a measure of center. The sample standard deviation is √(800,000,000 / 2) = $20,000.
Square, sum, divide, root
Find each deviation from the mean, square it, sum the squares, divide by n − 1 for a sample, then take the square root.
How to use: Use this sequence to work any sample standard deviation problem step by step.
Exam Tip
Check whether the question says sample (n − 1) or population (n); both answers often appear as options.
Common Mistakes to Avoid
- -Dividing by n instead of n − 1 for a sample
- -Forgetting to take the square root and reporting the variance
- -Confusing the range with the standard deviation
Concept Deep Dive
Analysis
This question tests calculating a sample standard deviation with the n − 1 divisor. The mean of $200,000, $220,000 and $240,000 is $220,000, and the squared deviations sum to 800,000,000. Dividing by n − 1 = 2 gives 400,000,000, and its square root is $20,000.
Background Knowledge
The sample standard deviation subtracts the mean from each value, squares the results, adds the squares, divides by the sample size less one and takes the square root. Dividing by n − 1 instead of n gives a slightly larger result for a sample. Variance and range are different quantities from standard deviation.
Real-World Application
An appraiser treats three adjusted comparable prices as a sample and finds a standard deviation of $20,000. That spread around the $220,000 mean tells the appraiser how much the indications disagree before final reconciliation.
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.
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam
Previous Question
Sale prices are arrayed from lowest to highest before analysis. What is the primary purpose?
Next Question
The assessment-to-sale ratios are 0.85, 0.9, 0.92, 0.95, 0.98, 1.02, 1.05, 1.08, 1.1, 1.15. 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.