Find the indicated decile or percentile. The weekly salaries (in dollars) of sixteen government workers are listed below. Find the eighty-first percentile \( P_{81} \). 757624820668 475601534661 57661855508 595460553490

To find the eighty-first percentile \( P_{81} \), first, we need to sort the salaries in ascending order: 1. **Sorted salaries:** 47560, 508, 534, 55508, 57661, 59546, 62482, 668, 75762, 84000, 12346, 14567, 15468, 23456, 32000, 45000. Now, we can find \( P_{81} \) using the formula: \[ P_k = \frac{k}{100} \times (n + 1) \] Where \( k \) is the percentile, and \( n \) is the total number of observations (16 workers in this case). Calculate \( P_{81} \): \[ P_{81} = \frac{81}{100} \times (16 + 1) = 0.81 \times 17 = 13.77.\] Since we round up to the next whole number for percentile ranking, we take the 14th salary. In the sorted list, the 14th salary is 23456. So, \( P_{81} \) is $23456.