February 13, 2017

# #1798: Box Plot

[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:

[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.]