Given the following comparable sales prices: $280,000, $285,000, $285,000, $290,000, $320,000, what is the mode?
Correct Answer
A) $285,000
The mode is the value that appears most frequently in the data set. $285,000 appears twice, more than any other value.
Why This Is the Correct Answer
Option A ($285,000) is correct because it appears twice in the dataset, making it the most frequently occurring value. When counting the frequency of each value: $280,000 appears once, $285,000 appears twice, $290,000 appears once, and $320,000 appears once. Since $285,000 has the highest frequency (2 occurrences), it is the mode of this dataset. The mode is specifically defined as the value that appears most often, regardless of its position in the ordered sequence.
Why the Other Options Are Wrong
Option B: $290,000
$290,000 appears only once in the dataset, so it cannot be the mode. While it may be close to the center of the data range, frequency of occurrence, not central position, determines the mode.
Option C: $292,000
$292,000 does not appear anywhere in the dataset and appears to be a calculated average. This suggests confusion between mode and mean (arithmetic average), which are completely different statistical measures.
Option D: $320,000
$320,000 appears only once in the dataset and is actually the highest value (outlier). This choice might reflect confusion between mode and maximum value, or misunderstanding that the mode must be the most frequent, not the highest value.
MODE = Most Often Displayed Example
Remember MODE as 'Most Often Displayed Example' - the mode is simply the value that shows up most often in your list. Think of it like the most popular item on a restaurant menu - it's the one that appears most frequently on orders.
How to use: When you see a list of numbers and need to find the mode, count how many times each number appears and pick the one with the highest count. If you see the acronym MODE, think 'Most Often Displayed Example' to remind yourself you're looking for frequency, not position or calculation.
Exam Tip
Always count the frequency of each value systematically rather than trying to identify the mode by visual inspection alone. Write down each unique value and tally marks next to them to avoid counting errors.
Common Mistakes to Avoid
- -Confusing mode with mean (average) and performing calculations instead of counting frequency
- -Confusing mode with median and looking for the middle value in an ordered list
- -Assuming the mode must be a calculated value rather than an actual data point from the set
Concept Deep Dive
Analysis
This question tests understanding of the mode, which is one of the three measures of central tendency (mean, median, mode) commonly used in real estate appraisal statistics. The mode represents the most frequently occurring value in a dataset and is particularly useful when analyzing comparable sales data to identify the most common price point in a market. In appraisal practice, the mode can help identify market preferences and typical buyer behavior patterns. Understanding measures of central tendency is essential for appraisers when analyzing market data and supporting valuation conclusions with statistical evidence.
Background Knowledge
The mode is one of three measures of central tendency used in statistics, alongside mean (average) and median (middle value). Unlike mean and median, the mode focuses solely on frequency of occurrence and can be applied to both numerical and categorical data. In real estate appraisal, understanding these statistical measures helps appraisers analyze comparable sales data and market trends effectively.
Real-World Application
When analyzing comparable sales in a neighborhood, an appraiser might find that most homes sold for $285,000, even though some sold for higher or lower amounts. This mode value of $285,000 indicates the most common market acceptance level and can support the appraiser's opinion of value, especially when the subject property is similar to those most frequently sold comparables.
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