1. The National Hockey League (NHL) consists of 30 teams. Teams earn points duri

Question

1. The National Hockey League (NHL) consists of 30 teams. Teams earn points during the regular season by playing 82 games against other teams in the league. If a game is decided in regulation, the winning team gets 2 points and the losing team gets 0. If the game is tied at the end of regulation, the game goes to overtime (and sometimes a shootout if necessary) the losing team gets 1 point In this case the eventual winning team gets 2 points and (a) Below is a frequency histogram of the final point totals for each of the teams at the end of the 2013-2014 season (this data is real) NHL Points 2013-2014 50 60 70 80 90 100 110 120 Total Regular Season Points STAT 224/324 In this histogram, the first bar on the left represents the closed interval [50, 55] points. This notation means that the first bar contains any number starting from exactly 50 to and including 55. The second bar from the left represents the interval (65,70] points, which means it does not contain 65 exactly but does contain everything from just above 65 up to and including 70. The remainder of the bars are defined similarly. Use this histogram to answer the next three questions. i. Give a range of possible values for the median. Make your answer as specific as possible ii. If this was a relative frequency histogram, what would be the height of the bar representing the interval (80, 85 points? It may be easiest to give your answer as a fraction. iii. If this was a density histogram, what would be the height of the bar representing the interval (80,85] points? It may be easiest to give your answer as a fraction.

Explanation / Answer

i)

Median is the middle value of ordered data set. There are 30 data values so median will be average of 15th and 16th data values. If we add up the freqeuncies of bars from 50 to 90 then we get:

1+2+2+4+5 = 14

By adding up the frequency of bar 90 to 95 is 14 + 4 = 18.

That is 15th and 16th data values lie in the interval (90, 95]. So possible range os median is (90, 95].

(ii)

The frequency for the bar (80, 85] is 4 so relative ferquency will be

4 /30 = 2/15

(iii)

The requried height is

4 / [30 * (85-80) ] = 4/ (30*5) = 2/ 75

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