Assessment-to-sale ratios are 0.88, 0.93, 0.96, 0.99, 1.02, 1.07, 1.11. Compute the arithmetic mean. Report as a decimal ratio to three places.
Correct Answer
B) 0.994
Sum=6.96; n=7; mean=6.96/7=0.9943. Common errors: using the median instead of the mean gives 0.990; using the midrange instead of the mean gives 0.995; dividing by 6 instead of 7 gives 1.160.
Why This Is the Correct Answer
Option B is correct because the sum of the ratios is 0.88 + 0.93 + 0.96 + 0.99 + 1.02 + 1.07 + 1.11 = 6.96. Dividing by the seven observations gives 6.96 / 7 = 0.9943, which is 0.994 to three places.
Why the Other Options Are Wrong
Option A: 0.990
Option A, 0.990, is the median, the middle (fourth) of the seven ordered ratios, used instead of the mean. The mean is 6.96 / 7 = 0.994.
Option C: 0.995
Option C, 0.995, is the midrange, (0.88 + 1.11) / 2, which uses only the lowest and highest ratios. The mean uses all seven values: 6.96 / 7 = 0.994.
Option D: 1.160
Option D, 1.160, comes from dividing the sum by 6 instead of 7 (6.96 / 6 = 1.160). There are seven ratios, so the mean is 6.96 / 7 = 0.994.
Add all, divide by all
The mean uses all values in the sum and all values in the count, so the divisor must match the number of items you added.
How to use: Use this to check your divisor in any mean calculation.
Exam Tip
Count the observations before dividing. Close distractors often come from the median or midrange, so make sure you used all values.
Common Mistakes to Avoid
- -Dividing by one less than the number of observations
- -Reporting the median as the mean
- -Averaging only the highest and lowest values
Concept Deep Dive
Analysis
This question tests the arithmetic mean of a set of assessment-to-sale ratios. Add all seven ratios and divide by seven. The distractors come from using a different measure of center or the wrong divisor.
Background Knowledge
The arithmetic mean is the sum of the observations divided by their number. The median is the middle value of ordered data, and the midrange is the average of the minimum and maximum. In a ratio study these are different measures of the overall level and can give slightly different results.
Real-World Application
An assessor reviews seven sales in a neighborhood and computes the mean assessment ratio of 0.994. Comparing it with the median of 0.990 helps show whether a few ratios are pulling the average in one direction.
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