Editing 1798: Box Plot

{{comic
| number    = 1798
| date      = February 13, 2017
| title     = Box Plot
| image     = box_plot.png
| titletext = You have to be careful doing this. Sometimes, when you push the whisker down, dynamite explodes.
}}

==Explanation==
This comic shows three vertical {{w|Box plot|box plots}} in the first panel, hence the title.

In {{w|descriptive statistics}}, a box plot is a convenient way of graphically depicting groups of numerical {{w|data}} through their {{w|quartiles}}. The second quartile is the {{w|median}} and it is not indicated in this comic, as it should be a line through the box (see the {{w|Quartile#Definitions|definitions of quartiles}}). But the top and bottom of the box is the first and third quartile, which splits the lowest/highest 25% off data of from the highest/lowest 75%, respectively. 

Box plots may also have lines extending vertically from the boxes (whiskers) indicating variability outside the upper and lower quartiles, (that is, the ''highest'' and ''lowest'' values in the data,) hence the terms box-and-whisker plot. These can be used to indicate the {{w|interquartile range}}, a measure of {{w|statistical dispersion}}. These have been included on the three boxes in the plot. 

The joke in the comic arises, because it turns out that the box plot is actually three real world objects and [[Cueball]] walks into the plot in the second panel, climbs up on the lower first box and on to the highest middle box. When the boxes are depicted in the orientation shown, the boxes can look like they are pumps, where the middle part, the box, can be pumped up. And Cueball does just that in the fourth panel, by pushing the top whisker down and when he leaves in the fifth and last panel, this box stays inflated, with the whisker visibly lower than in the first three panels, although higher than when he pushed it down in the fourth panel. (Inflating things that cannot be inflated was also the joke in [[1395: Power Cord]]. But as opposed to inflating the meaning of data, which many researchers sadly do in the real world, what [[Beret Guy]] does in that comic, is strictly [[:Category:Strange powers of Beret Guy|supernatural]].)

It could be said that the "data" in this comic was "inflated" and thus Cueball has been trying to show a smaller interquartile range than there actually is, thus inflating the possible conclusions that could be drawn from the data. 

The title text refers to how {{w|dynamite}}, an explosive, often used to have detonator boxes (aka. {{w|blasting machine}}s) which also looked similar to the top part of the box (without the lower whisker). These detonators were most commonly used for mining, with long wires leading to the explosives. Modern blasting machines are operated by push buttons and key switches, but the old push-handle design still resonates in the public consciousness today, due to its exposure in classic slapstick cartoon shorts like {{w|Looney Tunes}}, especially often used by {{w|Wile E. Coyote and the Road Runner|Wile E. Coyote}} against the Road Runner. See for instance here in the [https://youtu.be/0R66Fvhx0vQ?t=1m2s this compilation].

The title text also refers to so-called [http://users.stat.umn.edu/~rend0020/Teaching/STAT8801-2015Spring/handouts/24-dynamite.pdf dynamite plots]. This type of plot used to be very common in scientific publications, but since it hides most details about one's actual data, it is now frowned upon. The recommended alternative is the box plot.

The title text thus warns against this kind of data inflation, since sometimes it can go awry and lead to explosions. [[Randall]] has often made comics about presenting data as more important that they are, in one way or another, and this comics clearly falls into that category. See for example [[882: Significant]], [[1132: Frequentists vs. Bayesians]], [[1478: P-Values]] and [[1574: Trouble for Science]], and this one for manipulating the way data is presented: [[558: 1000 Times]].

A box plot was also used in [[539: Boyfriend]], maybe the only other time in xkcd. There are many other types of [[:Category:Charts|data carts]] that have their own subcategories, but not this type.

==Transcript==
:[A box plot with three vertical data points is shown. Each point consists of a shaded rectangular box, and a T-shaped whisker on each end.]

:[Cueball walks in; revealing that the box plot is a physical object which he looks up on.]

:[Cueball climbs on top of the diagram, holding onto the top whisker of the leftmost data point.]

:[Cueball, now standing upright on top of the box plot, bends over, grips the whisker of the center data point and starts pumping. The shaded box of the data point bulges. Cueball's movements are accompanied by sounds:]
:''Pump''
:''Pump''
:''Pump''

:[The box has been inflated so much that it almost touches the left and right data points. Cueball walks away.]

*'''Click''' to expand for a more detailed description:
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:[A box plot with three data points are shown. Each point consist of a standing rectangular box shaded gray and from each end of the box there extend a whisker which ends in a short line orthogonal to the whiskers line. The middle box is the longest and extends both above and below the other two, as does its whiskers. The first box is larger than the last, but those two are at the same level at their bottoms. But the bottom whisker of the first is longer than the last. If the middle box is about 1.9 cm high it will have a 1 cm whiskers below and an 0.8 cm whisker at the top for a total length of 3.7 cm. Then the first box would be 1.7 cm high with the bottom whisker 0.8 cm, and the top whisker 0.5 cm for a total length of 3 cm. The last box is then 1.4 cm high with the top whisker being 0.6 cm and the bottom 0.5 cm, for a total length of 2.5 cm. The boxes are 0.7 cm wide and the end lines for the whiskers are 0.5 cm wide. The data points stay in the same place and have the same dimensions through all five panels, except the middle point which changes as explained below in the last two panels.]

:[Cueball walks into the panel from the left looking up at the top of the first box.]

:[Cueball climbs on to the first box, by holding on to the top and stem of the first whisker, while putting a bend leg on the top of the box, while the other legs hangs down the side of the box.]

:[Cueball now stands on top of the plot, with one foot on the first box and a second foot on the middle box. He is bend over the whisker on the middle box, holding on to it with both hands, one on either side of the middle stem. He is pushing it up and down, as indicated with two light gray version of Cueball's arms and the stem, with the stem in the top gray version being about 0.1 cm above the original height and with Cueball thus with more bend arms than in the normal black version. He has thus pulled the "lever" a bit further up. The second gray version is in between these two, about 0.2 cm below the upper gray, and thus 0.1 cm below the original position and thus with a bit less bend arms that the top gray. In the final black version where the arms are almost stretched, the top is now only 0.5 cm over the box, 0.3 cm below the original position, further 0.2 cm below the second gray. On top of all this the middle box also increases its width bulging out in the top part with a maximum bulge around 0.6 cm below the top, to a width of 1.1 cm. That the movement of Cueball goes both ways are indicated both with 6 small double lines around Cueball's shoulders, arms and hands, but also by the sound his actions make.]

:[Finally Cueball has climbed down and walks away to the right, the panel panning a bit after him so the inflated box plot moves to the left in the panel. The middle box is now inflated evenly so the maximum bulge is at the middle and it is almost touching the other two boxes with a width of 1.4 cm, double the original thickness. There have all the time been 1.5 cm between the edges of the two other boxes, so the inflated box does not interfere with the other two, but is very close to their edges. The whisker at the bottom of the middle box is unchanged but the top whisker ended up being only 0.6 cm high, 0.2 cm lower than original position, but a 0.1 cm higher than when Cueball pushed down on it in the previous panel.]
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{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Charts]]
[[Category:Science]]
[[Category:Statistics]]