Question

The following are distances (in miles) traveled to 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) 15.5 and 27.2
B) 20 and 31
C) 13 and 40
D) 9 and 22

Answer 1

The 25th and 80th percentiles for the distances traveled to the workplace by employees are calculated by arranging the data in ascending order and using the percentile formula. The correct percentiles are approximately 8 for the 25th and 29 for the 80th, which corresponds closest to option B, 20 and 31.

Step-by-step explanation:

To find the 25th and 80th percentiles for the distances traveled to the workplace by employees, it is necessary to arrange the data in ascending order and then apply the percentile formula.

With the data provided, we first sort the distances: 2, 5, 6, 7, 9, 9, 10, 13, 15, 16, 18, 20, 22, 24, 25, 27, 31, 40.

For the 25th percentile, since there are 18 data points, we would calculate as follows:

P25 = 25/100 x (n+1), thus, 25/100 x (18+1) = 4.75, so it is between the 4th and 5th data points, which are 7 and 9.

We then average the two numbers.

The 25th percentile is (7+9)/2 = 8.

For the 80th percentile, 80/100 x (18+1) = 15.2, so it's between the 15th and 16th data points, which are 27 and 31.

Thus, the 80th percentile is (27+31)/2 = 29.

Therefore, the closest answer provided is B) 20 and 31.