Sale-price observations are $280,000, $285,000, $285,000, $290,000, $320,000. Compute the mode; use the uniquely most frequent observation. Report to the nearest dollar.
Correct Answer
D) $285,000
285000 occurs 2 times; every other distinct observation occurs less often.
Why This Is the Correct Answer
Option D is correct because $285,000 appears twice, while every other price appears only once. The mode is the value that occurs with the greatest frequency. It is therefore $285,000.
Why the Other Options Are Wrong
Option A: $292,000
Option A, $292,000, is the mean: ($280,000 + $285,000 + $285,000 + $290,000 + $320,000) ÷ 5 = $1,460,000 ÷ 5 = $292,000. The mode is the most frequent value, $285,000.
Option B: $280,000
Option B, $280,000, is the lowest observation and appears only once. The mode is $285,000, which appears twice.
Option C: $320,000
Option C, $320,000, is the highest observation and appears only once. The mode is $285,000, which appears twice.
Mode equals most
Mode and most both start with mo: the mode is the value that shows up most often.
How to use: Use the shared mo sound to recall that mode is about frequency.
Exam Tip
Look for repeated values first. If one option equals the arithmetic average, it is the mean distractor.
Common Mistakes to Avoid
- -Computing the mean instead of the mode
- -Picking an extreme value rather than the most frequent one
- -Assuming every data set has exactly one mode
Concept Deep Dive
Analysis
This question tests the mode, the most frequently occurring value. Count how many times each price appears and select the one that appears most often. Here exactly one value repeats, so the mode is unique.
Background Knowledge
The mode is the measure of central tendency based on frequency. A data set can have one mode, several modes or no mode if no value repeats. It is useful for identifying the most common price point or characteristic in a market.
Real-World Application
A builder sells many homes in a tract at $285,000, the base-model price. An appraiser notes this mode as the most common price point when describing the subdivision.
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