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StatisticsQ&A LibraryOutliers 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.Question

Asked Jan 16, 2020

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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.

Step 1

The values *Q*_{1} and *Q*_{3} represent the first and third quartile.

Generally the probability values of first quartile *Q*_{1} and third quartile *Q*_{3} 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 *Q*_{1} 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 *Q*_{3 }is 0.67.

The formula to find the interquartile range IQR is,

Step 3

The outlier values that are above *Q*3 by an amount ...

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