He following data give the annual salaries (in thousand dollars) of 20 randomly selected health care workers.

50 72 57 39 45 65 38 51 34 63 74 40 67 44 78 62 58 55 65 59

a. Calculate the values of the three quartiles and the interquartile range. Q1 = 44.5 Q2 = 57.5 Q3 = 65 IQR = 20.5

b. Find the approximate value of the 30th percentile. 45

c. Calculate the percentile rank of 62. %

Check it below

Step-by-step explanation:

1) Ordering it we have:

34  38  39  40  44  45  50  51  55  57  58  59  62  63  65  65 67  72  74  78

a) Then let's calculate the First Quartile by calculating the Median

Place the Median inside this row of values

34  38  39  40  44  45  50  51  55  57  57.5 58  59  62  63  65 65  67  72  74  78

Calculate the Median of the 10 salaries below the Median, to have the lower Quartile, i.e. <57.5

34  38  39  40  44  45  50  51  55  57

Do the Same with the values above 57.5, i.e. >57.5:

58  59  62  63  65  65 67  72  74  78

The Interquartile Range is the difference between the Upper and the Lower Quartile, so

b) The Value of the 30th percentile, is 0.3*N, so 0.3*(20)=6th position

6th position = 45

c) To find that let's set a table with this data, and check the Cumulative Frequency column. (Check the graph below)

The Salary of $62,000 is on the 65% percentile rank, only 35% of the annual salaries are  greater than $62,000