Answer
The ranked data set in increasing order is as follows:
35, 38, 39, 40, 44, 45, 50, 53, 55, 57 58, 59, 61, 62, 64, 64, 67, 71, 74, 77
The values of the three quartiles are:
Q1 =the median of the data smaller than Q2 = 44
Q2 = median = (10th+11th) / 2 + (57+58) /2= 57.5
Q3 =the median of the data larger than Q2 = 64
Interquartile range = Q3-Q1 = 64-44 = 20
The value of 57 lies in Q2 since it is less than Q2 but greater than Q1.
b. the value of the 30th percentile = $(30x20)\div100 = 6th = 45. $
30% of the annual salaries collected from 20 health care workers are less than 45 (thousand dollars).
c. Percentile rank of 61 = $(13\div20)x100% = 65%$, 65% of health care workers have the annual salaries less than 61 thousand dollars.
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