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Problem

There is no consistent way of defining an outlier that everyone agrees upon. For example, some people refer to an outlier that is any observation more than three standard deviations from the mean. Other people use the box plot definition, where an outlier (moderate or extreme) is any observation more than 1.5 IQR from the edges of the box, and some people care only about the extreme box plot-type outliers, those that are 3.0 IQR from the edges of the box. The file P02_18.xlsx contains daily percentage changes in the S&P 500 index over many years. Identify outliers—days when the percentage change was unusually large in either a negative or positive direction—according to each of these three definitions. Which definition produces the most outliers?

Step-by-step solution

Obtain the summary statistics for the percentage changes in S&P 500 index using Stat Tool in Excel. Add the data range as a stat tool range go to Stat tool Data Set Manager. A dialog box will appear. Click on NEW and in excel range box enter the range. The screenshot of the dialog box is given below;

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After this, click on OK button of it. Then, to obtain the descriptive statistics, go to Stat Tool Summary Statistics One variable Summary a dialog box will appear. Select the variable percent change. The screenshot of the dialog box is given below;

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Now, press OK. The screenshot of the summary statistics thus obtained is given as below,

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The first definition for outlier is an observation more than three standard deviation from the mean is an outlier. The number of observation lying beyond can be obtained using the command “=10619-COUNTIF(ST_change_3,"<0.03298")-COUNTIF(ST_change_3," <-0.03236")”. The result is 15 observations.

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The second definition is that any observation more than the first and third quartile is an outlier. The number of observation that lies beyond the range

can be calculated using the command

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that is, 558.

The third definition is that any observation more than the first and third quartile is an outlier. The number of observation that lies beyond the range

can be calculated using the command

that is, 202. Hence, the second definition produces most outliers.

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0 0

Chapter 2, Problem 56P

The file P02_56.xlsx contains monthly values of indexes that measure the amount of energy necessary to heat or cool buildings due to outside temperatures. (See the explanation in the Source sheet of the file.) These are reported for each state...

See solution

Chapter 2, Problem 3CQ

Does it make sense to construct a histogram for the state of residence of randomly selected individuals in a sample? Explain why or why not.

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