What does the mode represent in a statistical data set?
Correct Answer
C) The value that appears most frequently
An empirical mode is a value occurring with greatest frequency. There may be tied modes; a sample with no repeated value has no unique most-frequent observation. The median concerns ordered position, the arithmetic mean averages values, and the range is maximum minus minimum. Mode is not automatically the most appropriate summary for an appraisal conclusion.
Why This Is the Correct Answer
Option C is correct because the mode is the value that occurs with the greatest frequency in a data set. A data set can have tied modes, and one with no repeated value has no unique most-frequent observation.
Why the Other Options Are Wrong
Option A: The middle value when data is arranged in order
Option A, the middle value when data is arranged in order, defines the median. The median depends on ordered position, not frequency.
Option B: The arithmetic average of all of the values
Option B, the arithmetic average of all of the values, defines the mean. The mean adds all values and divides by the count.
Option D: The difference between highest and lowest values
Option D, the difference between highest and lowest values, defines the range. The range measures spread, not the most common value.
Mode equals most
Mode and most both start with M-O: the mode is the value that shows up most often.
How to use: Use this link to separate the mode from the median and mean on definition questions.
Exam Tip
Match each option to the statistic it defines before choosing; definition questions usually list several real statistics.
Common Mistakes to Avoid
- -Confusing the mode with the median
- -Assuming every data set has a single mode
- -Treating the mode as the arithmetic average
Concept Deep Dive
Analysis
This question tests the definitions of basic descriptive statistics. Each option defines a different statistic: median, mean, mode and range. You must match the mode to the value occurring most often.
Background Knowledge
The mode, median and mean are the three common measures of central tendency, each summarizing a data set differently. The mode is useful for identifying the most common characteristic, such as a typical bedroom count, but it is not automatically the best summary for an appraisal conclusion.
Real-World Application
An appraiser describing a subdivision notes that most homes have three bedrooms, making three the mode. This helps the appraiser identify the typical property that buyers in that market expect.
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.
Observed values are 100, 105, 110, 115, 120. Calculate the range (maximum−minimum).
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?
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An appraiser is developing an overall rate for a small warehouse from its physical components. Land sales indicate that the land represents 30% of total property value. Ground lease data indicate a land capitalization rate of 6%, and the building capitalization rate, including recapture, is 10%. Lenders on similar warehouses quote a 7.5% annual mortgage constant at a 70% loan-to-value ratio. What overall rate does the band of investment indicate?
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An appraiser is verifying the sale of an apartment building. The stated price of $1,600,000 consisted of $600,000 in cash and a $1,000,000 seller note at a below-market interest rate. The market value of the note is 96.25% of its face amount. The seller paid a $50,000 brokerage commission. Stabilized annual NOI is $125,000. What overall rate does this sale indicate?