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Select the outlier in the data set. $\newline$ $39, 49, 59, 60, 65, 72, 82, 456$ $\newline$ 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

39, 49, 59, 60, 65, 72, 82, 456

\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. $\newline$ The data set is: $39, 49, 59, 60, 65, 72, 82, 456$ . $\newline$ Clearly, $456$ is much larger than the other values. $\newline$ Outlier: $456$
Calculate Mean: Calculate the mean of the original data set. $\newline$ Mean = $(39 + 49 + 59 + 60 + 65 + 72 + 82 + 456) / 8$ $\newline$ Mean = $882 / 8 = 110.25$
Remove Outlier and Recalculate Mean: Remove the outlier and calculate the new mean. $\newline$ New data set: $39, 49, 59, 60, 65, 72, 82$ $\newline$ New mean = $(39 + 49 + 59 + 60 + 65 + 72 + 82) / 7$ $\newline$ New mean = $426 / 7 = 60.86$
Compare Original and New Mean: Compare the original mean to the new mean. $\newline$ Original mean: $110.25$ $\newline$ New mean: $60.86$ $\newline$ Since the new mean is lower, removing the outlier decreases the mean.

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