Sale prices are $200,000, $220,000, $240,000, $260,000, $280,000. Define percentile rank as (number strictly below the selected value ÷ total observations) × 100. What is the percentile rank of $240,000?
Correct Answer
D) 40.0%
Exactly 2 of 5 observations are strictly below $240,000. 2/5×100=40%. This explicitly excludes observations equal to the selected value.
Why This Is the Correct Answer
Option D is correct because two of the five prices ($200,000 and $220,000) are strictly below $240,000. The percentile rank is 2 ÷ 5 × 100 = 40.0%, and the stated definition excludes the observation equal to $240,000.
Why the Other Options Are Wrong
Option A: 60.0%
Option A, 60.0%, counts observations at or below $240,000: 3 ÷ 5 × 100 = 60.0%. The stated definition counts only values strictly below, giving 2 ÷ 5 × 100 = 40.0%.
Option B: 50.0%
Option B, 50.0%, assumes the median automatically sits at the 50th percentile rank. Under the stated definition, only 2 of 5 values are strictly below $240,000, giving 40.0%.
Option C: 33.3%
Option C, 33.3%, divides by n + 1 instead of the total number of observations: 2 ÷ 6 × 100 = 33.3%, borrowing a denominator from other percentile conventions. The stated definition divides by the 5 observations, giving 2 ÷ 5 × 100 = 40.0%.
Strictly below means skip yourself
When the rule says strictly below, do not count the value itself. Count only the values beneath it, then divide by all observations.
How to use: Use this when a percentile question defines its counting rule.
Exam Tip
Read the stated definition carefully; whether ties and the value itself are included decides between the close answer choices.
Common Mistakes to Avoid
- -Including the selected value in the count
- -Assuming the middle value is always at the 50th percentile rank
- -Dividing by n + 1 instead of the total number of observations
Concept Deep Dive
Analysis
This question tests applying a stated definition of percentile rank. Count only the observations strictly below the selected value, divide by the total number of observations and multiply by 100.
Background Knowledge
Percentile rank describes the share of observations falling below a given value. There is no single universally accepted method for computing percentiles, so the definition stated in the problem controls. Including or excluding the value itself changes the result.
Real-World Application
An appraiser describes where a subject's expected price falls among five neighborhood sales. Using the client's stated definition, the appraiser reports a 40th percentile rank and notes the convention used.
More Statistics Questions
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