Question

The following are distances (in miles) traveled to the workplace by 16 employees of a certain hospital. 40, 27, 22, 28, 3, 7, 15, 2, 29, 1, 10, 18, 20, 18, 32, 25 Find 10th and 75th percentiles for these distances. (If necessary, consult a list of formulas.) (a) The 10th percentile: miles (b) The 75th percentile: miles X ?

Answer 1

a)

10^th percentile = 2

Solution:

Step 1. Arrange the data in ascending order: 1, 2, 3, 7, 10, 15, 18, 18, 20, 22, 25, 27, 28, 29, 32, 40

Step 2. Compute the position of the p^th percentile (index i):

i = (p / 100) * n), where p = 10 and n = 16

i = (10 / 100) * 16 = 1.6

Step 3. The index i is not an integer, round up. (i = 2) ⇒ the 10^th percentile is the value in 2^th position, or 2

Answer: the 10^th percentile is 2

b)

75^th percentile = 27.5

Solution:

Step 1. Arrange the data in ascending order: 1, 2, 3, 7, 10, 15, 18, 18, 20, 22, 25, 27, 28, 29, 32, 40

Step 2. Compute the position of the p^th percentile (index i):

i = (p / 100) * n), where p = 75 and n = 16

i = (75 / 100) * 16 = 12

Step 3. The index i is an integer ⇒ the 75^th percentile is the average of the values in the 11^th and 12^th positions (27 and 28 respectively)

Answer: the 75^th percentile is (27 + 28) / 2 = 27.5

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