Question

The following are distances (in miles) traveled to the workplace by 18 employees of a certain hospital. 5, 13, 24, 31, 9, 18, 6, 40, 16, 20, 10, 25, 15, 22, 7, 2, 27, 9. Find the 25th and 80th percentiles for these distances.

a) 12, 24.6
b) 9.5, 28.4
c) 10.5, 31.2
d) 8, 35.2

Answer 1

The 25th percentile for the distances traveled by the employees is 9 miles and the 80th percentile is 24 miles.

Step-by-step explanation:

To find the 25th and 80th percentiles for the distances traveled by the employees, you need to first arrange the distances in ascending order:

2, 5, 6, 7, 9, 9, 10, 13, 15, 16, 18, 20, 22, 24, 25, 27, 31, 40.

The 25th percentile is the value that is greater than or equal to 25% of the data. To find this, multiply 25% by the total number of data points (18) and round up to the nearest whole number. So, 25% of 18 is 4.5, which rounds up to 5. Therefore, the 25th percentile is the 5th value, which is 9 miles.

The 80th percentile is the value that is greater than or equal to 80% of the data. To find this, multiply 80% by the total number of data points (18) and round up to the nearest whole number. So, 80% of 18 is 14.4, which rounds up to 15. Therefore, the 80th percentile is the 15th value, which is 24 miles.