The following data set represents sale prices: $280,000, $290,000, $290,000, $295,000, $340,000. What is the mode?
Correct Answer
A) $290,000
The mode is the value that appears most frequently in the data set. $290,000 appears twice, more than any other value.
Why This Is the Correct Answer
$290,000 is the correct answer because it appears twice in the dataset ($280,000, $290,000, $290,000, $295,000, $340,000), while all other values appear only once. By definition, the mode is the value with the highest frequency of occurrence. Since $290,000 has a frequency of 2 and all other values have a frequency of 1, $290,000 is definitively the mode. This makes the dataset unimodal with a clear single mode.
Why the Other Options Are Wrong
Option B: $299,000
$299,000 is incorrect because this value does not even appear in the dataset. The mode must be an actual value from the data set, not a calculated average or interpolated number. This appears to be the mean of the dataset, which is a different measure of central tendency entirely.
Option C: $295,000
$295,000 is incorrect because it appears only once in the dataset. While it is the median (middle value when arranged in order), it is not the mode since it doesn't have the highest frequency of occurrence.
Option D: $280,000
$280,000 is incorrect because it appears only once in the dataset. Although it is the lowest value in the range, frequency of occurrence, not position or magnitude, determines the mode.
MODE = Most Often Data Entry
Remember MODE as 'Most Often Data Entry' - the value that shows up most often in your data entries. Think of it as the 'popular kid' in the dataset who appears at the party (dataset) more times than anyone else.
How to use: When you see a statistics question asking for the mode, immediately scan the dataset and count how many times each number appears. The number with the highest count wins - it's the 'Most Often Data Entry.'
Exam Tip
Always count the frequency of each value systematically, making tick marks next to repeated values to avoid missing duplicates in longer datasets.
Common Mistakes to Avoid
- -Confusing mode with median (middle value) or mean (average)
- -Selecting a calculated value that doesn't actually appear in the dataset
- -Failing to count frequencies carefully and missing repeated values
Concept Deep Dive
Analysis
This question tests understanding of the mode, one of the three primary measures of central tendency used in real estate appraisal statistics. The mode represents the most frequently occurring value in a dataset and is particularly useful when analyzing categorical data or when the most common value is more meaningful than the average. In real estate, the mode can help identify the most common price point in a neighborhood or the most frequent property type sold. Unlike mean and median, a dataset can have no mode (if all values appear equally), one mode (unimodal), or multiple modes (bimodal or multimodal).
Background Knowledge
Appraisers must understand measures of central tendency (mean, median, mode) to analyze comparable sales data and market trends effectively. The mode is particularly valuable when identifying the most common price range or property characteristics in a market area, helping appraisers understand typical buyer preferences and market patterns.
Real-World Application
When analyzing comparable sales in a subdivision, an appraiser might find that $350,000 appears most frequently among recent sales, indicating this is the modal price point and suggesting strong market acceptance at this level, even if some outliers sold for much higher or lower amounts.
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