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# Math Lesson 3: Displaying Data Graphically - page 9 / 11

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32

66

80 83.5

98

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100

Can you see the spread of the bottom 50% of the scores? [32 to 80] The top 50% of the scores? [80 to 98] The middle 50% of the scores? [66 to 83.5] The bottom 25% of the scores? [32 to 66] The top 25% of the scores? [32 to 66]

The calculator computes the five-number-summary each time you go to STAT/CALC/1-Var Stats/ENTER. After entering the list number in which the data are stored, press ENTER. Scroll down past the n= and find the five-number summary.

Your calculator will also graph a box-and-whisker plot for your data. Press 2nd/y= and turn one of the plots ON (arrow and press ENTER). Under Type: arrow to the middle plot of the second row and press ENTER. Your cursor will be next to Xlist. Enter there the name of the list in which you have your data stored (e.g. L1). Press ZOOM 9 to graph and you will see your box plot. Use the TRACE button to see the five-number summary as you arrow through the box plot.

# E. Outliers

Did you notice the score of 32 in Mr. Sneed’s class? Was this an unusual score for the class? In other words, was there perhaps some explanation for this low score (such as a long absence on the part of the student)? Maybe the score should not be included in the data set if it resulted from some unusual circumstance and if we want to get a truly reliable picture of how Mr. Sneed’s class is doing. A score that differs significantly from most of the data entries is often considered an outlier. Sometimes it is best to eliminate it from the data set. For example, suppose you we entering heights in inches for students in your class into a list on your calculator, and instead of entering 65 you entered 6 by mistake. The inclusion of a data entry of 6 inches would greatly throw off your measure of center. (Which measure of center would it have the most effect on – mean or median?) It should be eliminated from the data set or be corrected.

But what about the score of 56 in Mrs. Short’s class? Is that an outlier? Often an outlier stands away from the rest of the data in a dot plot or stem-and-leaf plot. But how do we know if a score is far enough away, or different enough from the rest of the data, to be considered a legitimate outlier? There is a mathematical rule that will allow you to make the determination so that you don’t have to guess.

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