Observed values are 12, 15, 18, 15, 20, 22, 15. Compute the mode; use the uniquely most frequent observation. Report to three decimal places.
Correct Answer
A) 15.000
15 occurs 3 times; every other distinct observation occurs less often.
Why This Is the Correct Answer
Option A is correct because 15 occurs three times, while every other value (12, 18, 20 and 22) occurs only once. The most frequent value is the mode, reported as 15.000.
Why the Other Options Are Wrong
Option B: 16.714
Option B, 16.714, is the arithmetic mean: (12 + 15 + 18 + 15 + 20 + 22 + 15) / 7 = 117 / 7 = 16.714. The mode is the most frequent value, 15.
Option C: 12.000
Option C, 12.000, is the lowest value and occurs only once. The mode is 15, which occurs three times.
Option D: 22.000
Option D, 22.000, is the highest value and occurs only once. The mode is 15, which occurs three times.
Mode means most
Mode and most both start with mo: the mode is the value that shows up most often.
How to use: Use this to separate the mode from the mean and median.
Exam Tip
Tally each value's frequency; do not compute anything else when the question asks for the mode.
Common Mistakes to Avoid
- -Computing the mean instead of the mode
- -Picking an extreme value
- -Confusing the mode with the median
Concept Deep Dive
Analysis
This question tests the mode, the value that occurs with the greatest frequency. The candidate counts how often each value appears and picks the most frequent one. The distractors are the mean and the two extremes.
Background Knowledge
The mode is the value that appears most often in a data set. A set can have one mode, several modes or none if no value repeats. The mode is useful for describing the most common characteristic, such as a typical bedroom count in a neighborhood.
Real-World Application
An appraiser describing a subdivision notes that three-bedroom homes are the mode among recent sales. This helps establish that the subject's three-bedroom layout conforms to the neighborhood.
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