Statistic and Probability

Question

Thirteen internists in the Midwest are randomly selected, and each internist is asked to report last

year’s income. The incomes obtained are:

216000, 240000, 122000, 135000, 166000, 236000, 227000, 224000, 136000, 186000, 223000, 206000, 210000

a) Find 90th percentile (3 marks)

b) Find the median (3 marks)

c) Find the first quartile (3 marks)

d) Find the third quartile (3 marks)

e) Find the 10th percentile (3 marks)

f) Find the interquartile range (3 marks)

g) Develop a five-number summary (3 marks)

h) Construct the boxplot (6 marks)

Answer 1

First step is to write data in order. Each data value occupies a slot from 1 to 13.

To find slot number corresponding to any percentile, use formula (percentile/100) * (14).

a) for 90th percentile, slot number would be (90/100) * 14 = 12.6. Since between slot numbers, compute average of numbers in 12th and 13th slots.

b) median is the 50th percentile, slot number would be (50/100)*14 = 7.

c) first quartile is 25th percentile, slot number would be (25/100)*14 = 3.5. (average values of 3rd and 4th slot)

d) third quartile is 75th percentile, slot number would be (75/100)*14 = 10.5. (average values of 10th and 11th slot)

e) for 10th percentile, slot number would be (10/100) * 14) = 1.4 (average values of 1st and 2nd slots)

f) interquartile range = third quartile - first quartile

g) five number summary = minimum, 1st quartile, median, 2nd quartile, maximum