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Thirty-nine home sizes are listed in increasing order. Using the index formula i = (k/100)(n + 1) for the 25th percentile, which value in the list is the first quartile?
AThe average of the 9th and 10th values
BThe 10th value in the ordered list
CThe 25th value in the ordered list
DThe average of the 10th and 11th values
Answer & Solution
Correct answer: B. The 10th value in the ordered list
1. The first quartile is the 25th percentile, so use k = 25 and n = 39 in the index formula.
2. Compute the index: i = (25/100)(39 + 1) = 0.25 x 40 = 10.
3. The index is a whole number, so no averaging is needed.
4. The first quartile is exactly the 10th value in the ordered list.
5. Option D applies the rounding-and-averaging rule, which is only used when the index is not an integer.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.2 Measures of the Location of the Data_
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