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Box and Whisker Plots

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A box and whisker plot is used to display data. Explain what box and whisker plots shows us. Provide example. Thanks.

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By example, this solution explains a box and whisker plot and what the data displayed tells us.

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1. A box and whisker plot is used to display data. Explain, by example, what box and whisker plots show us. Thanks.

A box-and-whisker plot (often simply called a box plot) is a graphical way of showing data. It is useful for quickly finding outliers - data points out of line with the rest of the data set.

Suppose we want to construct a box plot of the following test scores:

50, 60, 73, 77, 80, 81, 82, 83, 84, 84, 84, 85, 88, 95, 100

If they're not already in numerical order, it's best to arrange them in ascending order.

First, we need to construct the "box." To do so, we must find the upper and lower quartiles and the median. The median is the number in the middle of our set (when arranged in numerical order). The upper and lower quartiles are the values 1/4 of the way from the top or bottom of our set. In our example:

50, 60, 73, 77, 80, 81, 82, 83, 84, 84, 84, 85, 88, 95, 100
^ ^ ^
L.Q. Median U.Q.

To draw the box, we'll put a scale on the x-axis and draw a box from the lower quartile to the upper quartile. We'll add a vertical line to mark the median, like so:

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