# Staistics

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Problem 3

John Tukey, the mathematician who came up with the idea of the stem and leaf plot, developed several other methods that were brilliant combinations of simplicity and effectiveness. One such is the box plot, also known as a box and whisker plot. It is, not surprisingly, a diagram that looks like a box, and its goal is to give a quick sense of the shape of a distribution. A box plot consists of a box whose edges are at the lower and upper quartiles; within the box there is a heavy line at the median. The whiskers’’ are lines that extend from the lower quartile to the minimum value, and from the upper quartile to the maximum (though sometimes they go only as far as a low percentile and the corresponding high percentile instead of the min and the max).

It’s easier to see what’s going on in a picture, so here is a set of box plots of data on the speed of light, measured repeatedly in several experiments by the physicists Michelson and Morley. It’s a well-known figure; you’ll even find a version of it in the Wikipedia entry for the box plot. In our version, the whiskers extend to the ends of the data.

There are five box plots, each summarizing the data from one experiment. The vertical axis shows the variable: the speed of light in km/sec, minus 299,000. That’s to make the scale manageable; it’s easier to think about a number like 900 than 299,900. You saw this kind of move before, in the gravity data in Chapter 3 of your text.

Let’s focus on Experiment 1. The minimum speed recorded was 650 (on the scale described above), the lower quartile was 850, the median was 940, the upper quartile was 980, and the maximum was 1070. Start from the low end of the bottom whisker of the boxplot for Experiment 1, and you will find that these numbers agree with what you see on the graph.

: 4.0 points

a) Which of the experiments had the lowest median measurement?

Experiment 1Experiment 2Experiment 3Experiment 4Experiment 5

b) The speeds in one of the experiments had a lower quartile of 800, a median of 840, and an upper quartile of 880. Which experiment was it?

Experiment 1Experiment 2Experiment 3Experiment 4Experiment 5