Appraisal Statistical Methods

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?

Observed sale prices are $450,000, $475,000, $425,000, $500,000, $440,000. Calculate the range (maximum−minimum), to the nearest dollar.

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.

Observed values are 100, 105, 110, 115, 120. Calculate the range (maximum−minimum).

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?

The sale-price range is $45,000 and the maximum is $385,000. Find the minimum price.

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.

The positive observations are 10, 15, 22.5. Compute their simple geometric mean (product of all observations)^(1/n). Report as a dimensionless ratio to three decimals.

Assessment-to-sale ratios are 0.88, 0.93, 0.96, 0.99, 1.02, 1.07, 1.11. Compute the arithmetic mean. Report as a decimal ratio to three places.

A ratio study has an arithmetic mean assessment-to-sale ratio of 1.02 and a sale-price-weighted mean ratio of 1. Compute PRD = arithmetic mean ÷ weighted mean; report three decimals.

Assessment-to-sale ratios are 1.2, 1.1, 1, 0.9; corresponding sale prices are $100,000, $200,000, $300,000, $400,000 in the same order. Compute PRD as the arithmetic mean ratio divided by the sale-price-weighted mean ratio. Round to two decimals.

Sale-price observations are $410,000, $420,000, $435,000, $450,000. Compute the median; order the observations first and average the two middle values if n is even. Report to the nearest dollar.

Before materially relying on sales from a commercial database, what approach best addresses data reliability?

Sale prices are $255,000, $280,000, $300,000, $320,000, $355,000. Using the median of each half including the overall median (Tukey hinges), Q1=$280,000 and Q3=$320,000. Compute the interquartile range Q3−Q1, to the nearest dollar.

Sale prices are $190,000, $210,000, $230,000, $250,000, $270,000, $300,000, $360,000. Using the median of each half excluding the overall median, Q1=$210,000 and Q3=$300,000. Compute the interquartile range Q3−Q1, to the nearest dollar.

Assessment-to-sale ratios are 0.94, 1.09, 0.98, 1.03, 1.06. Compute the median; order the observations first and average the two middle values if n is even. Report as a decimal ratio to three places.

The positive observations are $160,000, $250,000. Compute their simple geometric mean (product of all observations)^(1/n). Report to the nearest dollar.

Two advertisements quote asking prices but the actual closed consideration is uncertain. Which step best addresses the actual completed sale price?

The assessment-to-sale ratios are 0.86, 0.94, 1, 1.06, 1.14. 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.

A sale-price distribution has fourth central moment m4 = 229,635,000 in (thousands of dollars)^4 and second central moment m2 = 8100 in (thousands of dollars)^2. Compute excess kurtosis m4 / m2² − 3. Use moments with the same population (N) divisor, not an unbiased sample variance; report two decimals.

Observed sale prices are $180,000, $185,000, $190,000, $195,000, $200,000. Calculate the range (maximum−minimum), to the nearest dollar.

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.

The assessment-to-sale ratios are 0.9, 0.95, 1.05, 1.1. 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.

The assessment-to-sale ratios are 0.9, 0.94, 0.98, 1.02, 1.06, 1.1. 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.

Sale-price mean is $510,000, mode $420,000 and standard deviation $90,000. Calculate Pearson's first skewness coefficient (mean − mode) / standard deviation, to two decimals.

An appraiser is summarizing ten verified sales of similar homes, which sold for $210,000, $240,000, $250,000, $260,000, $270,000, $280,000, $290,000, $300,000, $400,000 and $640,000. One colleague calculates a trimmed mean and another a winsorized mean, each treating one observation in each tail. What are the correct results?

The arithmetic mean is $400,000 and sample standard deviation is $20,000. Compute the coefficient of variation s/mean, expressed as a decimal ratio. Report three decimals.

Five sale prices are $390,000, $410,000, $420,000, $430,000, $520,000. Remove the single smallest and single largest price, then calculate the mean of the remaining three. Report to the nearest dollar.

Which statistic is the middle ordered numerical observation when n is odd, and the average of the two middle observations when n is even?

Sale prices are arrayed from lowest to highest before analysis. What is the primary purpose?

An analysis excludes 15 of 60 sales without explanation. What is the concern?

Sale-price observations or stated extremes are $370,000, $510,000. Compute the midrange (minimum+maximum)/2 to the nearest dollar.

In an approximately normal distribution, roughly what share of observations falls within one standard deviation of the mean?

How should an appraiser handle numerical precision when applying a statistically estimated adjustment?

Which consideration supports treating a sales sample as representative of a defined market population?

For positive assessment-to-sale ratios, define COD as 100 × mean absolute deviation from their median ÷ median. How does it differ from the median ratio?

Assume permission and licensing requirements have been satisfied. Before relying on a third-party market study, which step addresses its analytical reliability?

Four parcels have assessed value/sale price pairs of $120,000/$100,000, $210,000/$200,000, $255,000/$300,000 and $300,000/$400,000. Compute each assessment-to-sale ratio. Define PRD as their arithmetic mean divided by total assessed value/total sale price. Which rounded PRD and observed sample tendency follow?

Sale-price observations are $185,000, $192,000, $188,000, $195,000, $190,000. Compute the median; order the observations first and average the two middle values if n is even. Report to the nearest dollar.

The assessment-to-sale ratios are 0.88, 0.92, 0.96, 0.98, 1.02, 1.04, 1.08, 1.12. 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.

The assessment-to-sale ratios are 0.9, 0.9, 0.95, 1, 1, 1.05, 1.05. 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 0.85, 0.92, 1, 1.08, 1.15; corresponding sale prices are $500,000, $400,000, $300,000, $200,000, $100,000 in the same order. Compute PRD as the arithmetic mean ratio divided by the sale-price-weighted mean ratio. Round to two decimals.

The assessment-to-sale ratios are 0.9, 0.95, 1, 1.05, 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.

Eight sales in a market area, in ascending order of price, sold for $210,000, $230,000, $245,000, $260,000, $275,000, $290,000, $310,000, $340,000. By the nearest-rank method, which takes the lowest price at or below which at least 70% of the sales fall, what is the 70th percentile?