For 29 ordered ages the index for the 83rd percentile is 24.9. The 24th age is 71 and the 25th is 72. What is the 83rd percentile?

1. The index 24.9 is not a whole number, so it is rounded both down and up. 2. Rounding down gives position 24 and rounding up gives position 25. 3. The age in position 24 is 71 years and the age in position 25 is 72 years. 4. Averaging them gives 143 divided by 2, which is 71.5 years. 5. Taking 72 years alone would mean rounding the index up only, which the rule does not allow. 6. A value of 74.7 years comes from treating 24.9 as an age rather than as a position. _Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.2 Measures of the Location of the Data_