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# Box Plot Simulation

Module by: David Lane. E-mail the author

## General Instructions

The displayed boxplot is based on the data shown on the left side of the screen. Notice that various aspects of the boxplot such as the mean and median are labeled. These labels can be hidden by unchecking the "show labels on boxplot" button.

Beneath the data is a pair of buttons that let you specify whether you want to be able to enter data or to see statistics based on the data. You can modify the data or delete it all (by pressing the "Clear All button") and enter your own data. Your data can be typed in or pasted in from another application. When pasting, you must use the keyboard shortcut for pasting (Command-V for Mac, CTRL-V for Windows. When you change the data, the boxplot will disappear. After you have entered new data, click the "Draw boxplot" button to redraw the boxplot.

Modify the data in various ways and see how it affects the boxplot. Try putting in some extreme values and see if they get labeled as outliers. Outside values are shown as "o's" beyond the inner fence. Far out values are shown as *'s outside the outer fence.

## Step by Step Instructions

Recall that the upper fence is 1 step above the upper hinge and that a step is 1.5 times the difference between the upper and lower hinges (the H-Spread). For these data, the H-Spread is 23 -15 = 8. So, the upper fence is (1.5)(8) = 12 above the upper hinge of 23. That makes it 23 + 12 = 35. Click on the "statistics button" to see that the value of the upper fence is 35. The upper adjacent is the largest value below this fence and is equal to 33 since 33 is the highest value below 35. Notice that there is one outside value (beyond the upper inner fence). How high would the value have to be in order to be classified as a far-out value. Try increasing the highest value and see. To be an outside value, a score must be 2 steps above the upper hinge. That means it must be greater than 23 + (2)(12) = 47. Change the highest value from 37 to 48 and notice that it is now classified as a far-out value. Change the second highest value from 33 to 37. It now becomes an outside value.

The lowest value is 6. How low would it have to be to be an outside value? Change it to 4 and see what happens. It is still above the inner fence of 3. Why is the inner fence 3? It is one step below the lower hinge. That is, 15 - 12 = 3. Make the lowest score 2 and you will see that it is an outside value. Make it -10 and it is a far out value.

## Summary

The H-spread is the difference between the 75th and 25th percentiles. A step is 1.5 times the H-spread. The inner fences are each one step from a hinge; the outer fences are two steps. Whiskers extend from hinges to adjacent values.

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