Khan/khan-exercises — Issue #9859: Creating box and whisker plots - Video inconsistent with answer/explanation
Author: KhanBugz
Created: 2011-12-30 01:57:47+00:00
State: open
Labels: chrome, win7, wrong-or-unclear

Reporter: rjacobson@ymail.com

The problem asked me to construct a bar & whisker chart of the following 15 data points (after I sorted them):

{3,5,7,7,9,9,9,9,9,9,9,10,10,12,14}

The median is located between the bars here, with the "left" and "right" each sides having 7 data points.

{3,5,7,7,9,9,9,|9|,9,9,9,10,10,12,14}

Obviously, the minimum is 3, and the maximum is 14.

Concerning how to calculate the position of the left and right bars for the 25% and 75% quartiles, the instructions on Sal's video appear to be inconsistent with the "correct" answer for this problem, including the official "explanation."

According to Sal's video, the left bar (i.e., the mark for the 25% quartile) should be the median of all of the points left of the median number, *inclusive* of the lowest number. See Sal's explanation at 04:20 to 5:20 of the video, which discussed taking the median of "the set that's smaller than six," inclusive of the first number -- i.e., the set inclusive of both "1s" {1, 1, 2, 2, 3, 3, 4, 4}.

According to these instructions, the correct position of the left-hand bar for this example should be calculated as the median of the set inclusive of the digit "3" -- i.e., of the following set: {3,5,7,7,9,9,9}.

By this methodology, the left bar should be 7. However, the exercise gives 7 as the wrong answer for the left-hand bar.

According to the official "explanation" for this exercise, the correct answer is "8." It calculates 8 as the median of the following set: {5,7,7,9,9,9}. I.e., it calculates the left-hand bar as the median of the set *exclusive* of the lowest/first data point.

This is inconsistent with the video. According to the methodology in the video, it should be the median of {3,5,7,7,9,9,9}.

I checked the Wikipedia entry for bar-and-whisker charts, and I couldn't immediately tell which is actually the "correct" answer. Either way, the explanation in the video seems inconsistent with the approach in the answers to the practice questions. Could you please clarify which approach is correct?

I hate to be pedantic, by the way. This is a fantastic website, and I really appreciate all of the work you're doing. Perhaps you could create a new badge, "Annoying Pedant," for people who submit corrections like these. :-)

[creating_box_and_whisker_plots.html?seed=75&problem=0](http://sandcastle.khanacademy.org/media/castles/Khan:master/exercises/creating_box_and_whisker_plots.html?seed=75&problem=0&debug)

[Answer timeline](http://sandcastle.khanacademy.org/media/castles/Khan:master/exercises/creating_box_and_whisker_plots.html?seed=75&problem=0&debug&activity=%5B%5B%22incorrect-activity%22%2C%22%5B3%2C7%2C9%2C10%2C14%5D%22%2C187%5D%2C%5B%22hint-activity%22%2C%220%22%2C4%5D%2C%5B%22hint-activity%22%2C%220%22%2C6%5D%2C%5B%22hint-activity%22%2C%220%22%2C10%5D%2C%5B%22hint-activity%22%2C%220%22%2C11%5D%2C%5B%22hint-activity%22%2C%220%22%2C19%5D%5D)

[[3,7,9,10,14]]

Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKit/535.7 (KHTML, like Gecko) Chrome/16.0.912.63 Safari/535.7

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