# Outliers For the purposes of constructing modified boxplots as described in Section 3–4, outliers are defined as data values that are above q3 by an amount greater than 1.5 × IQR or below q1 by an amount greater than 1.5 × IQR, where IQR is the interquartile range. Using this definition of outliers, find the probability that when a value is randomly selected from a normal distribution, it is an outlier.

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Outliers For the purposes of constructing modified boxplots as described in Section 3–4, outliers are defined as data values that are above q3 by an amount greater than 1.5 × IQR or below q1 by an amount greater than 1.5 × IQR, where IQR is the interquartile range. Using this definition of outliers, find the probability that when a value is randomly selected from a normal distribution, it is an outlier.

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Step 1

The values Q1 and Q3 represent the first and third quartile.

Generally the probability values of first quartile Q1 and third quartile Q3 are 0.25 and 0.75, respectively.

Step 2

Use Standard normal (z) distribution table to find the z scores.

Procedure:

For the area to the left of 0.25,

• Locate the nearest value of 0.25 in the body of the Table.
• Move left until the first column and note the value as –0.6.
• Move upward until the top row and note the value as 0.07.

Thus, the z score for Q1 is –0.67.

Procedure:

For the area to the left of 0.75,

• Locate the nearest value of 0.75 in the body of the Table.
• Move left until the first column and note the value as 0.6.
• Move upward until the top row and note the value as 0.07.

Thus the z score for Q3 is 0.67.

The formula to find the interquartile range IQR is,

Step 3

The outlier values that are above Q3 by an amount ...

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