Twenty-nine ages are listed in order. The position for the 70th percentile is 0.70 multiplied by 30. Which position is that?
AThe 20th
BThe 23rd
CThe 21st
DThe 30th
Answer & Solution
Correct answer: C. The 21st
1. The index rule multiplies the percentile as a decimal by one more than the count.
2. There are 29 ages, so one more than the count is 30.
3. The 70th percentile gives a decimal of 0.70.
4. Multiply 0.70 by 30.
5. Seven tenths of 30 is 21.
6. So the 70th percentile sits at the 21st position in the ordered list.
7. Answering 20 uses 0.70 times 29 and forgets to add one to the count first.
8. Answering 30 quotes the count plus one rather than the position it leads to.
_Source: OpenStax High School Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics" and Ch 3 "Probability Topics", section 2.3 Measures of the Location of the Data_
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