Assessment-to-sale ratios are 0.88, 0.94, 1.02, 1.08, 1.2. Compute the median; order the observations first and average the two middle values if n is even. Report as a decimal ratio to three places.
Correct Answer
B) 1.020
Ordered values: 0.88, 0.94, 1.02, 1.08, 1.2. The middle observation is 1.02. Common errors: using the mean instead of the median gives 1.024; using the midrange instead of the median gives 1.040; averaging the two values around the middle although n is odd gives 1.010.
Why This Is the Correct Answer
Option B is correct because the ordered ratios are 0.88, 0.94, 1.02, 1.08 and 1.20, and with five observations the median is the third value. That middle observation is 1.02, reported to three places as 1.020.
Why the Other Options Are Wrong
Option A: 1.010
Option A, 1.010, comes from averaging the two values around the middle, (0.94 + 1.08) / 2 = 1.010, even though n is odd. With five observations the median is the single middle value, 1.020.
Option C: 1.024
Option C, 1.024, is the arithmetic mean, 5.12 / 5 = 1.024, rather than the median. The median is the middle ordered value, 1.020.
Option D: 1.040
Option D, 1.040, is the midrange, (0.88 + 1.20) / 2 = 1.040, which uses only the two extremes. The median is the middle ordered value, 1.020.
Odd Count, One Middle
An odd count has one true middle seat, so the median is that single value; only an even count needs two values averaged.
How to use: Use this check before averaging anything when computing a median.
Exam Tip
Order the data first and count the observations to decide whether the median is a single value or an average of two.
Common Mistakes to Avoid
- -Averaging the two values around the middle when n is odd
- -Reporting the mean instead of the median
- -Forgetting to sort the values before picking the middle
Concept Deep Dive
Analysis
This question tests computing a median for an odd number of observations. After ordering, the median is the single middle value; there is no averaging when n is odd. The distractors come from substituting other location measures or averaging values incorrectly.
Background Knowledge
The median is the value of the middle item in an odd number of items arranged by size, or the average of the two central items in an even number. It is a resistant measure of location and is preferred in ratio studies because extreme ratios do not pull it.
Real-World Application
An appraiser reviewing five assessment-to-sale ratios for a subdivision computes the median ratio of 1.020 to describe the typical assessment level. Because one ratio is 1.20, the median gives a steadier summary than the mean.
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