Question

The table below shows the heights, in inches, of 15 randomly selected National Basketball Association (NBA) players and 15 randomly selected Division I National Collegiate Athletic Association (NCAA) players.

NBA	84	77	80	76	81	81	77	85
	78	79	78	79	84	75	77
NCAA	79	74	74	79	78	77	76	75
	75	82	76	78	78	79	73

Using the same scale, draw a box-and-whisker plot for each of the two data sets, placing the second plot below the first.

Write a valid conclusion based on the data.

A. The median height of an NCAA player is very close to the third-quartile height of an NBA player.

B. The median height of an NBA player is very close to the median height of an NCAA player.     

C. The third-quartile height of an NBA player is very close to the first-quartile height of an NCAA player.

D. The median height of an NBA player is very close to the third-quartile height of an NCAA player.

Answer 1

Solution Given, and Heights Heights of 15 NBA players (in inches) 84, 77,80, 76,81,81,77,85, 78, 79, 78,79,84, 75, 77 of 15 NCAA players (in inches) 79, 74, 74, 79, 78, 77, 76, 75, 75, 82, 76, 78, 78, 79,73 We will draw box and whisker plot for each of the two data sets. (is For NBA players :- First, we will order the set i.e. 75, 76, 77,77,77, 78, 78, 79,79.80,81,81,84,84,85 Since, Here 15 values in this set. middle value (eight value )7g, is median. [second quartile = median = 79 197 Now, the first half has seventh values. so, middle value (fourth value) 77 is first quartile. (9, = 77 Second half has also seventh values. middle value (fourth value) 81 is Third quartile. [@=81 are So,

we ( (ii) For NCAA players (in inches) : - First will order the set. 73, 74, 74, 75, 75, 76, 76, 77, 78, 78, 78, 79, 79, 79,82 (first half) (second half) since, here are 15 values in this set. So, middle value (eight valul) 77 is median. [median Q = 77 middle value of first half is 75. first quartile [@, = 75 middle value of second half is 79. Third quartile [@z = 79] (For NBA players) > (For NCAA) So So of! players Q cz M + 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86. (box and whisker plot) from above plot, we can say that "The median neight of an NBA player is very close to third-quartile height of an NCAA player". [option- (1) is correct]