Which statistic is the middle ordered numerical observation when n is odd, and the average of the two middle observations when n is even?
Correct Answer
B) Median value
The median is the middle observation in an ordered odd-sized numerical sample, or the arithmetic mean of the two middle observations for an even-sized sample. Mode concerns frequency; mean averages all values; range measures maximum minus minimum. The median is less sensitive to extremes than the mean, but the most useful summary depends on the analytical purpose.
Why This Is the Correct Answer
Option B is correct because the median is the middle observation in an ordered sample with an odd count, and the average of the two middle observations when the count is even. It marks the point with half the data below and half above. It is less sensitive to extreme values than the mean.
Why the Other Options Are Wrong
Option A: Modal value
Option A, the modal value or mode, is the value that occurs most often. It is based on frequency, not on position in the ordered data.
Option C: Mean value
Option C, the mean value, adds all the values and divides by the count. It uses every observation's size rather than selecting the middle position.
Option D: Overall range
Option D, the overall range, is the maximum minus the minimum. It measures spread, not the center of the data.
Mode most, median middle
Mode sounds like most (most frequent); median sounds like middle (middle position); mean is the average.
How to use: Use these sound-alikes to match each term with its definition.
Exam Tip
Any definition built around the middle ordered position points to the median. Range is a spread measure, not a center.
Common Mistakes to Avoid
- -Confusing the median with the mode
- -Treating the range as a measure of center
- -Forgetting to average the two middle values when n is even
Concept Deep Dive
Analysis
This question tests recognition of the median from its definition. The middle ordered value for an odd count and the average of the two middle values for an even count describe the median exactly. Candidates must distinguish it from the mode, the mean and the range.
Background Knowledge
The three common measures of central tendency are the mean, median and mode. The median depends only on the order of the data, which makes it resistant to outliers. The most useful summary depends on the purpose of the analysis and the shape of the data.
Real-World Application
A market report states a median sale price for a county where a few luxury sales would inflate the mean. Readers get a typical price that is not distorted by those high-end transactions.
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?
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