What is the mean of the following sale prices: $245,000, $252,000, $238,000, $265,000, and $250,000?
Correct Answer
A) $250,000
The mean is the sum of all values divided by the number of values: ($245,000 + $252,000 + $238,000 + $265,000 + $250,000) ÷ 5 = $1,250,000 ÷ 5 = $250,000.
Why This Is the Correct Answer
Option A ($250,000) is correct because it represents the accurate calculation of the arithmetic mean. The sum of all five sale prices ($245,000 + $252,000 + $238,000 + $265,000 + $250,000) equals $1,250,000. When this total is divided by the number of data points (5), the result is exactly $250,000. This demonstrates the proper application of the mean formula: sum of all values divided by the count of values.
Why the Other Options Are Wrong
Option B: $252,000
Option B ($252,000) is incorrect because it represents one of the individual sale prices from the dataset rather than the calculated mean. This is a common error where test-takers might confuse an individual data point with the average, or possibly make an arithmetic mistake in their calculation.
Option C: $247,500
Option C ($247,500) is incorrect and likely results from a calculation error, possibly from incorrectly adding the sale prices or dividing by the wrong number. This value is close to the correct answer but demonstrates the importance of careful arithmetic in appraisal calculations.
Option D: $245,000
Option D ($245,000) is incorrect because it simply represents the lowest sale price in the dataset rather than the calculated mean. This suggests confusion between identifying individual data points versus calculating the central tendency measure.
SUM-COUNT Method
Remember 'SUM then COUNT' - Add up all the values (SUM), then divide by how many values you counted (COUNT). Think of it as 'sharing equally' - if you had to split all the sale prices equally among the number of sales, each would get the mean amount.
How to use: When you see a mean calculation question, immediately write down 'SUM ÷ COUNT' at the top of your work area, then systematically add all values and divide by the total number of values. Always double-check your addition before dividing.
Exam Tip
Always show your work step-by-step: write out the addition of all values, show the sum, then show the division. This helps prevent calculation errors and allows you to check your work quickly.
Common Mistakes to Avoid
- -Adding the numbers incorrectly due to rushing
- -Dividing by the wrong count (forgetting to count all values)
- -Confusing the mean with one of the individual sale prices in the answer choices
Concept Deep Dive
Analysis
This question tests the fundamental statistical concept of calculating the arithmetic mean (average), which is essential in real estate appraisal for analyzing comparable sales data. The mean provides a central tendency measure that helps appraisers understand the typical value range of similar properties in a market area. Understanding how to calculate and interpret the mean is crucial for the sales comparison approach, which is one of the three primary valuation methods used in real estate appraisal. Appraisers frequently use mean calculations when analyzing multiple comparable sales to establish a reasonable value range for the subject property.
Background Knowledge
The arithmetic mean is one of three primary measures of central tendency (along with median and mode) used extensively in real estate appraisal and market analysis. Appraisers must be proficient in basic statistical calculations to properly analyze comparable sales data and support their valuation conclusions with quantitative evidence.
Real-World Application
Appraisers use mean calculations when analyzing comparable sales to establish value ranges for properties. For example, when appraising a single-family home, an appraiser might calculate the mean sale price of 5-10 comparable properties to help determine the subject property's market value and to identify any outliers that might need special consideration.
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