What is the mean of the following sale prices: $245,000, $252,000, $238,000, $265,000, and $250,000?
Correct Answer
C) $250,000
Why this is correct: The mean (average) is calculated by summing all values and dividing by the count. Sum: $245,000 + $252,000 + $238,000 + $265,000 + $250,000 = $1,250,000. Divide by 5: $1,250,000 ÷ 5 = $250,000. Why the other choices are wrong: "$252,000" is one of the data points, not the mean. "$245,000" is another data point. "$247,500" might be a miscalculation, such as averaging only four numbers or an incorrect sum. Exam tip: For mean calculations, always double-check your sum before dividing. On the exam, quickly estimate to catch obvious errors.
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 A: $252,000
Option A ($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 B: $245,000
Option B ($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.
Option D: $247,500
Option D ($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.
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.
More Statistics Questions
A building cost $2,500,000 to construct 8 years ago. Using straight-line depreciation over a 40-year life, what is the current depreciated value?
The following sale prices were recorded: $245,000, $250,000, $250,000, $255,000, $280,000. What is the mode?
A property has a replacement cost of $1,800,000. Physical deterioration is estimated at $200,000, functional obsolescence at $150,000, and external obsolescence at $100,000. What is the depreciated value using the breakdown method?
What is the present value of $150,000 to be received in 5 years, assuming a discount rate of 8%?
A triangular lot has a base of 100 feet and a height of 80 feet. What is the area in square feet?
An irregular lot can be divided into a rectangle (100' × 80') and a triangle (base 60', height 40'). What is the total area in acres?
A property has a net operating income of $85,000 and annual debt service of $68,000. What is the debt coverage ratio?
A warehouse has interior dimensions of 120 feet × 80 feet × 20 feet high. What is the volume in cubic feet?
A property is purchased for $500,000 with a loan of $400,000. What is the loan-to-value ratio?
A property sold for $400,000 with annual gross rent of $40,000. What is the gross rent multiplier?
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam
Related Tools
Previous Question
A building cost $800,000 to construct 15 years ago and has an estimated total economic life of 60 years. Using the age-life method, what is the accrued depreciation?
Next Question
The following sale prices were recorded: $285,000, $295,000, $275,000, $285,000, $305,000. What is the mode?