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Select the outlier in the data set. $\newline$ $5, 75, 77, 79, 80, 83, 88, 90, 96$ $\newline$ 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

5, 75, 77, 79, 80, 83, 88, 90, 96

\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 in the given data set: $5, 75, 77, 79, 80, 83, 88, 90, 96$ . To find the outlier, we can look for a number that is significantly different from the rest of the data. In this case, the number $5$ stands out as it is much lower than all other numbers.
Calculate Mean with Outlier: Calculate the mean of the data set with the outlier included. $\newline$ Mean = $(5 + 75 + 77 + 79 + 80 + 83 + 88 + 90 + 96) / 9$ $\newline$ Mean = $673 / 9$ $\newline$ Mean $\approx 74.78$
Calculate Mean without Outlier: Calculate the mean of the data set without the outlier $5$ . $\newline$ Mean without outlier = $\frac{75 + 77 + 79 + 80 + 83 + 88 + 90 + 96}{8}$ $\newline$ Mean without outlier = $\frac{668}{8}$ $\newline$ Mean without outlier = $83.5$
Compare Means: Compare the two means to determine if the mean would increase or decrease upon the removal of the outlier. The mean without the outlier ( $83.5$ ) is greater than the mean with the outlier ( $74.78$ ). Therefore, removing the outlier would increase the mean.

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