Given the following data set: 12, 15, 18, 15, 22, 15, 20. What is the mode?
Correct Answer
A) 15
The mode is the value that appears most frequently in a 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. Looking at the data set 12, 15, 18, 15, 22, 15, 20, we can count that 15 appears three times, while all other values (12, 18, 22, 20) appear only once each. Since 15 has the highest frequency of occurrence, it is the mode of this dataset.
Why the Other Options Are Wrong
Option B: 16.7
Option B (16.7) is incorrect because this represents the mean (average) of the dataset, not the mode. The mean is calculated by adding all values and dividing by the number of values, which gives (12+15+18+15+22+15+20)÷7 = 16.7, but this is a different measure of central tendency.
Option C: 18
Option C (18) is incorrect because while 18 appears in the dataset, it only occurs once. The mode must be the most frequently occurring value, and 18 does not meet this criterion since 15 appears three times compared to 18's single occurrence.
Option D: 22
Option D (22) is incorrect because 22 appears only once in the dataset. Like option C, this value does not qualify as the mode since it is not the most frequently occurring value in the data set.
MODE = Most Often Detected Entry
Remember MODE as 'Most Often Detected Entry' - the mode is always the value that shows up most often in your data. Think of it like the most popular house style in a neighborhood - it's the one you see most frequently.
How to use: When you see a 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 - don't calculate averages or look for middle values.
Exam Tip
Always count frequencies systematically by going through the dataset and tallying each unique value. Write down your counts to avoid errors, especially with larger datasets.
Common Mistakes to Avoid
- -Confusing mode with mean (average) and performing mathematical calculations instead of counting frequencies
- -Selecting the median (middle value) when data is arranged in order rather than the most frequent value
- -Choosing the highest or lowest value in the dataset instead of the most frequently occurring value
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 one of three primary measures of central tendency alongside mean and median. In appraisal practice, understanding the mode helps identify the most common property characteristics, sale prices, or market conditions within a dataset. Unlike mean and median which require mathematical calculations, the mode is determined simply by counting frequency of occurrence.
Background Knowledge
Measures of central tendency include mean (average), median (middle value), and mode (most frequent value), each providing different insights into data distribution. In real estate appraisal, these statistical measures help analyze comparable sales, rental rates, and market trends to support valuation conclusions.
Real-World Application
In appraisal practice, mode helps identify the most common property features in a market area, such as the most frequent number of bedrooms, bathrooms, or the most common sale price range, which assists in determining typical market expectations and buyer preferences.
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