Assessment-to-sale ratios are 0.96, 0.98, 0.99, 1.01. Compute the arithmetic mean. Report as a decimal ratio to three places.
Correct Answer
B) 0.985
Sum=3.94; n=4; mean=3.94/4=0.985. Common errors: dividing by 3 instead of 4 gives 1.313; dividing by 5 instead of 4 gives 0.788; not dividing the sum by the count gives 3.940.
Why This Is the Correct Answer
Option B is correct because the sum is 0.96 + 0.98 + 0.99 + 1.01 = 3.94, and 3.94 ÷ 4 = 0.985. The arithmetic mean is the sum of the observations divided by their number. Here there are four ratios, so the divisor is 4.
Why the Other Options Are Wrong
Option A: 0.788
Option A, 0.788, comes from dividing by 5 instead of 4: 3.94 ÷ 5 = 0.788. With four ratios, the mean is 3.94 ÷ 4 = 0.985.
Option C: 1.313
Option C, 1.313, comes from dividing by 3 instead of 4: 3.94 ÷ 3 ≈ 1.313. With four ratios, the mean is 3.94 ÷ 4 = 0.985.
Option D: 3.940
Option D, 3.940, is the sum without dividing by the count. The mean is 3.94 ÷ 4 = 0.985.
Sum then share
Add everything up, then share it equally among the number of observations.
How to use: Use this for any arithmetic mean calculation, double-checking the count.
Exam Tip
A mean of ratios that all sit near 1.00 should also be near 1.00; an answer like 1.313 or 3.940 is a sign of a counting or division error.
Common Mistakes to Avoid
- -Dividing by the wrong number of observations
- -Forgetting to divide the sum by the count
- -Mistaking the sum for the mean
Concept Deep Dive
Analysis
This question tests computing the arithmetic mean of four ratios. Add the values to get 3.94 and divide by the count of 4. The distractors come from dividing by the wrong count or not dividing at all.
Background Knowledge
The arithmetic mean is the most familiar measure of central tendency but is more affected by extreme values than the median. In ratio studies it is one of several level measures. Counting observations correctly is essential to computing it.
Real-World Application
An assessor computes the mean of four assessment-to-sale ratios in a small subdivision to compare with the median. The close agreement suggests no extreme ratios are distorting the level estimate.
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