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Thirteen ordered house prices have a median of 488,800. The lower half runs 114,950; 158,000; 230,500; 387,000; 389,950; 479,000. What is the first quartile?
AQ1 = 308,750
BQ1 = 230,500
CQ1 = 388,475
DQ1 = 387,000
Answer & Solution
Correct answer: A. Q1 = 308,750
1. The first quartile is the middle value of the lower half of the ordered data.
2. The lower half holds six prices, so there is no single middle price.
3. The two central prices of that half are 230,500 and 387,000.
4. Averaging them gives 617,500 divided by 2, which is 308,750, so a quartile need not be one of the observed prices.
_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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