Question

a. obtain the quartiles b. determine the interquartile range c. find the five-number summary d. identify potential outliers, if any e. construct a boxplot. 3.121 The Great Gretzky. Wayne Gretzky, a retired profes- sional hockey player, played 20 seasons in the National Hockey League (NHL), from 1980 through 1999. S. Berry explored some of Gretzky's accomplishments in "A Statistician Reads the Sports Pages" (Chance, Vol. 16, No. 1, pp. 49-54). The following table shows the number of games in which Gretzky played during each of his 20 seasons in the NHL. 79 80 80 80 80 80 79 64 73 78 74 45 48 80 82 82 74 78 81 70

Answer 1

Solution(a)
First sort the data from smallest to largest data value as follows:
45,48,64,70,73,74,74,78,78,79,79,80,80,80,80,80,80,81,82,82
n = 20
Quartile 1 or Q1 can be calculated as
Q1 = (n+1)/4 = (20+1)/4 = 5.25th value i.e. 5th value is 73 and 6th value is 74 so 5.25th value is 73+0.25*(74-73) = 73.25
Q2 or Median = (n+1)/2 = (20+1)/2 = 10.5th value i.e. 10th value is 79 and 11thy value is 79 so median is 79
Q3 = 3*(n+1)/4 = 3*(20+1)/4 = 15.75th value i.s. 15th value is 80 and 16th value is 80 so Q3 = 80
Solution(b)
Interquatile range can be calculated as
IQR = Q3 - Q1 = 80 - 73.25 = 6.75
Solution(c)
five number summary can be calculated as
Minimum = 45
Q1 = 73.25
Median = 79
Q3 = 80
Maximum = 82
so five number summary is 45,73.25,79,80,82
Solution(d)
Lower fence = Q1 - 1.5 * IQR = 73.25 - 1.5*6.75 = 63.125
Upper fence = Q3 + 1.5*IQR = 80+1.5*6.75 = 90.125
Any value which is not between 63.125 and 90.125 than this valus is outlier.
So outliers are 45 and 48
Solution(e)

82 44