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Select the outlier in the data set. $\newline$ $21, 26, 28, 29, 32, 33, 35, 609$ $\newline$ If the outlier were removed from the data set, would the mean increase or decrease? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease

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Identify an outlier and describe the effect of removing it

Full solution

Q. Select the outlier in the data set.

\newline

21, 26, 28, 29, 32, 33, 35, 609

\newline

If the outlier were removed from the data set, would the mean increase or decrease?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

Identify Outlier: Identify the outlier by comparing each value to the rest of the data set. The data set is: $21, 26, 28, 29, 32, 33, 35, 609$ . The value $609$ is much larger than all other values and is therefore the outlier.
Calculate Mean with Outlier: Calculate the mean of the data set including the outlier. $\newline$ Mean = $(21 + 26 + 28 + 29 + 32 + 33 + 35 + 609) / 8$ $\newline$ Mean = $(813) / 8$ $\newline$ Mean = $101.625$
Calculate Mean without Outlier: Calculate the mean of the data set without the outlier. $\newline$ Mean without outlier = $(21 + 26 + 28 + 29 + 32 + 33 + 35) / 7$ $\newline$ Mean without outlier = $(204) / 7$ $\newline$ Mean without outlier $\approx 29.14$
Compare Means: Compare the means to determine if the mean would increase or decrease when the outlier is removed. $\newline$ The mean without the outlier ( $29.14$ ) is less than the mean with the outlier ( $101.625$ ), so the mean would decrease if the outlier were removed.

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