Given the following data set: 12, 15, 18, 15, 20, 22, 15. What is the mode?
Correct Answer
A) 15
The mode is the value that appears most frequently in the data set. The number 15 appears three times, more than any other value.
Why This Is the Correct Answer
Option A (15) is correct because the mode is defined as the value that appears most frequently in a dataset. When examining the given data set (12, 15, 18, 15, 20, 22, 15), we can count the frequency of each number: 12 appears once, 15 appears three times, 18 appears once, 20 appears once, and 22 appears once. Since 15 appears three times, which is more than any other value in the dataset, 15 is the mode. This demonstrates the fundamental principle that mode is determined by frequency of occurrence, not by numerical value or position.
Why the Other Options Are Wrong
Option B: 16.7
Option B (16.7) is incorrect because this appears to be the mean (average) of the dataset, not the mode. The mean is calculated by adding all values (12+15+18+15+20+22+15 = 117) and dividing by the number of values (117÷7 = 16.7). While 16.7 is a valid measure of central tendency, it represents the arithmetic average, not the most frequently occurring value.
Option C: 18
Option C (18) is incorrect because while 18 is present in the dataset, it only appears once. The mode must be the most frequently occurring value, and since 18 appears only once compared to 15 which appears three times, 18 cannot be the mode. This represents a common confusion between identifying values present in the dataset versus identifying the most frequent value.
Option D: 10
Option D (10) is incorrect because 10 does not appear anywhere in the given dataset (12, 15, 18, 15, 20, 22, 15). The mode must be a value that actually exists in the dataset and appears most frequently. Since 10 is not even present in the data, it cannot possibly be the mode.
MODE = Most Often Displayed Element
Remember MODE as 'Most Often Displayed Element' - the value that shows up the MOST in your data set. Think of it as the 'popular kid' in school who appears most frequently in group photos.
How to use: When you see a statistics question asking for the mode, immediately start counting how many times each number appears in the dataset. The number with the highest count is your mode - the 'Most Often Displayed Element.'
Exam Tip
Always count the frequency of each value systematically by going through the dataset number by number, making tally marks or writing down counts to avoid missing any occurrences.
Common Mistakes to Avoid
- -Confusing mode with mean (average) - mode is about frequency, not calculation
- -Selecting a value that appears in the dataset but not most frequently
- -Choosing a number that doesn't even exist in the given dataset
Concept Deep Dive
Analysis
This question tests understanding of measures of central tendency, specifically the mode, which is fundamental to statistical analysis in real estate appraisal. The mode represents the most frequently occurring value in a dataset and is particularly useful when analyzing categorical data or identifying the most common characteristics in comparable sales. Unlike the mean (average) or median (middle value), the mode focuses on frequency of occurrence rather than numerical position or calculation. Understanding the mode is essential for appraisers when analyzing market data, identifying typical property features, or determining the most common sale prices in a neighborhood.
Background Knowledge
Measures of central tendency include mean (average), median (middle value), and mode (most frequent value), each serving different analytical purposes in real estate appraisal. The mode is particularly valuable when dealing with categorical data or when identifying the most common characteristics in a market analysis.
Real-World Application
In real estate appraisal, mode is used to identify the most common sale price range in a neighborhood, the most frequent number of bedrooms in comparable properties, or the most typical lot size in a subdivision, helping appraisers understand market preferences and typical buyer expectations.
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