Ordered sale prices are $300,000, $320,000, $340,000, $360,000, $380,000, $400,000, $420,000, $440,000, $460,000, $480,000, $500,000, $520,000, $540,000, $560,000, $580,000, $600,000, $620,000, $640,000, $660,000, $680,000. Using the nearest-rank method, which takes the lowest price at or below which at least 5% of the sales fall, what is the 5th percentile?
Correct Answer
C) $300,000
r=ceil(0.05×20)=1; observation 1 is $300,000. A different percentile convention can yield a different answer, so the stated nearest-rank method controls.
Why This Is the Correct Answer
Option C is correct because there are 20 ordered prices, so the rank is r = ceil(0.05 × 20) = ceil(1) = 1. The first ordered observation is $300,000, so that is the 5th percentile under this method.
Why the Other Options Are Wrong
Option A: $320,000
Option A, $320,000, is the second observation. It would result from moving up one position even though 0.05 × 20 = 1 exactly, so no rounding is needed; the rank is 1 and the value is $300,000.
Option B: $490,000
Option B, $490,000, is the median, the average of the 10th and 11th prices, ($480,000 + $500,000) / 2. The 5th percentile sits at rank ceil(0.05 × 20) = 1, which is $300,000.
Option D: $380,000
Option D, $380,000, is the fifth ordered observation; it comes from reading the "5th percentile" as the 5th position in the list. The rank must be computed first: r = ceil(0.05 × 20) = 1, which points to $300,000.
Rank first, then read
Compute the rank number by rounding p × n up, then count down the ordered list to that position and read off the value.
How to use: Use this whenever a question names the nearest-rank method and gives an ordered list.
Exam Tip
Apply the exact convention stated in the question. If p × n is already a whole number, rounding up leaves it unchanged.
Common Mistakes to Avoid
- -Adding one to a rank that is already a whole number
- -Treating the percentile number as the position in the list
- -Confusing a low percentile with the median
Concept Deep Dive
Analysis
This question tests a stated percentile rule. With the nearest-rank method, the rank is p × n rounded up, and the percentile is the observation at that position. Because percentile conventions differ, the method named in the question controls the answer.
Background Knowledge
A percentile is a value below which a given share of the data falls. There is no single universally accepted way to compute percentiles; methods differ in how they handle positions that fall between observations. The nearest-rank method uses r = ceil(p × n) and returns an actual observed value.
Real-World Application
An appraiser summarizing 20 neighborhood sales reports the low end of the price distribution using a nearest-rank percentile. Stating the method in the report lets a reader reproduce the $300,000 figure.
More Statistics Questions
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