A weighted mean differs from a simple mean in that the weighted mean:
Correct Answer
B) Gives more influence to observations judged more reliable
Why this is correct: A weighted mean assigns different weights (importance) to each data point based on judgment, such as giving more influence to sales that are more comparable or reliable. A simple (arithmetic) mean gives equal weight to every observation. Why the other choices are wrong: "Always produces a higher value than a simple arithmetic mean" is wrong; weighting can produce a higher or lower value depending on the weights assigned. "Uses only the highest and lowest observations" describes the midrange, not a weighted mean. "Requires that the sample be normally distributed" is not a requirement for calculating a weighted mean. Exam tip: Weighting is a formal way to reconcile comparables; the weights must be supported by your analysis.
Why This Is the Correct Answer
A weighted mean gives more influence to observations judged more reliable, which is exactly its purpose and exactly what distinguishes it from a simple mean. The weights encode the appraiser's judgment about data quality and comparability. That judgment must be explained rather than merely asserted, so that a reviewer can evaluate the weighting rather than just the result. Used properly it is a transparent way to document reconciliation.
Why the Other Options Are Wrong
Option A: Always produces a higher value than a simple arithmetic mean
A weighted mean can land above, below, or exactly on the simple mean depending entirely on which observations receive the heavier weights. If the most reliable sales happen to be the lowest indications, the weighted mean falls below the simple mean. The word always is the disqualifier and the claim has no basis in the arithmetic.
Option C: Uses only the highest and lowest observations
Using only the highest and lowest observations describes the midrange, a crude measure of central tendency that discards everything in between. A weighted mean uses every observation, merely at differing influence. Confusing the two would throw away most of the data.
Option D: Requires that the sample be normally distributed
Normality is an assumption underlying certain inferential procedures such as confidence intervals and hypothesis tests, not a precondition for computing a weighted average. A weighted mean is a descriptive calculation that works on any set of numbers with any distribution. The option imports an inferential requirement into a descriptive statistic.
Weights Are Judgments With Numbers
A weighted mean is the appraiser's reasoning made arithmetic. Each weight says how much you trust that observation. Because the weights come from judgment, they need explanation just as any adjustment does.
How to use: When a question contrasts a weighted mean with a simple mean, answer in terms of unequal influence. Reject options that predict a direction, describe a different statistic, or impose a distributional requirement.
Exam Tip
Reconciliation is never required to be a mechanical average, weighted or otherwise. If an item asks how to reconcile, the answer involves judgment about reliability, not an arithmetic recipe.
Common Mistakes to Avoid
- -Assigning weights without explaining the reasoning behind them
- -Treating a mechanical average of comparables as reconciliation
- -Confusing the weighted mean with the median or the midrange
Concept Deep Dive
Analysis
A simple arithmetic mean treats every observation as equally informative, summing the values and dividing by their count. A weighted mean multiplies each observation by a weight reflecting its importance or reliability, sums those products, and divides by the sum of the weights. The distinction matters in appraisal because comparables are never equally reliable: one sale may be nearly identical to the subject and verified with a party to the transaction, while another required large adjustments and was confirmed only from public records. Assigning more weight to the first is a formal way of expressing what reconciliation does qualitatively. The important discipline is that the weights themselves must be supported by reasoning the appraiser can articulate, typically the magnitude of gross adjustment, the recency of the sale, the quality of verification, and the similarity of location and physical characteristics. It is also worth remembering that appraisal reconciliation is not required to be arithmetic at all; the appraiser may conclude at a point within the range of indications based on judgment, and often does.
Background Knowledge
You need the measures of central tendency, mean, median, mode, and midrange, and the mechanics of a weighted mean. You should also know that reconciliation weighs indications by appropriateness, accuracy, and quantity of evidence, and that averaging comparables mechanically is not reconciliation.
Real-World Application
An appraiser with five adjusted indications assigns the heaviest weight to two sales requiring under five percent gross adjustment and verified with the listing agents, lighter weight to two requiring larger adjustments, and minimal weight to an older sale, then explains the basis for each weight in her reconciliation.
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