Observed values are 100, 105, 110, 115, 120. Calculate the range (maximum−minimum).
Correct Answer
A) 20.00
120−100=20. The range is a spread measure; the average or maximum alone does not answer the question.
Why This Is the Correct Answer
Option A is correct because the range is the maximum minus the minimum: 120 − 100 = 20. It describes how far apart the extreme observations are.
Why the Other Options Are Wrong
Option B: 110.00
Option B, 110.00, is the mean (and median) of the five values, (100 + 105 + 110 + 115 + 120) ÷ 5 = 110, which is a measure of location. The range is 120 − 100 = 20.
Option C: 120.00
Option C, 120.00, is just the maximum value, not the difference between the maximum and minimum. The range is 120 − 100 = 20.
Option D: 10.00
Option D, 10.00, subtracts the mean from the maximum (120 − 110 = 10), which measures how far the top value sits above the average rather than the full spread. The range subtracts the minimum: 120 − 100 = 20.
Highest minus lowest
The range is just the highest value minus the lowest value. If your answer is one of the data values, you have a location, not a spread.
How to use: Use this to quickly eliminate choices that equal the mean or the maximum.
Exam Tip
Range questions often include the mean and the maximum as distractors. Make sure your answer is a difference between two values.
Common Mistakes to Avoid
- -Reporting the mean instead of the range
- -Reporting the maximum value alone
- -Subtracting the mean instead of the minimum from the maximum
Concept Deep Dive
Analysis
This question tests the definition of the range as a simple measure of spread. Identify the largest and smallest observations and subtract; measures of location such as the mean or the maximum do not answer a spread question.
Background Knowledge
The range is the simplest measure of dispersion, equal to the largest value minus the smallest value. Because it depends only on the two extremes, a single unusual observation can change it substantially. Appraisers often pair it with more robust spread measures such as the interquartile range.
Real-World Application
An appraiser notes that adjusted sale prices for five comparables span from $100,000 to $120,000 per unit. Reporting the range of $20,000 quickly shows the client how wide the indicated values are before reconciliation.
More Statistics Questions
An undamaged but functionally inadequate system causes a supported $60,000 loss. Replacement costs $85,000 and restores only $60,000, with no other benefits. What loss classification and deduction fit?
The subject is a 10-year-old dwelling with improvement cost new of $640,000. A highly comparable 7-year-old dwelling recently sold for $580,000; at the sale date its site was worth $150,000 and its improvement cost new was $500,000. Market evidence shows depreciation accruing evenly with actual age. What is the depreciated value of the subject improvements?
Observed sale prices are $450,000, $475,000, $425,000, $500,000, $440,000. Calculate the range (maximum−minimum), to the nearest dollar.
For an arithmetic illustration only, depreciate a historical $2,000,000 construction cost on a zero-salvage straight-line 40-year schedule for 10 years. What unindexed scheduled amount remains? This is not a conclusion of current market value or current replacement cost.
For an arithmetic illustration, allocate historical construction cost $2,400,000 over 40 years on a zero-salvage equal annual schedule. After 8 years, what scheduled unindexed amount remains? This is not a current market-value conclusion.
For an arithmetic schedule only, allocate historical cost $2,500,000 over 40 years with zero residual. After 8 years, what unindexed scheduled amount remains? This is not an estimate of current market value.
The sale-price range is $45,000 and the maximum is $385,000. Find the minimum price.
A property is purchased for $1,500,000 with a loan of $1,200,000. Using the purchase price as the value, what is the loan-to-value ratio, as a percentage to one decimal?
Improvement cost new is $1,800,000. Separately supported improvement depreciation deductions of $200,000, $150,000, $100,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
Improvement cost new is $500,000. Separately supported improvement depreciation deductions of $125,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
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
For an arithmetic illustration, allocate historical construction cost $2,400,000 over 40 years on a zero-salvage equal annual schedule. After 8 years, what scheduled unindexed amount remains? This is not a current market-value conclusion.
Next Question
The sale-price range is $45,000 and the minimum is $235,000. Find the maximum price.