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Select the outlier in the data set. $\newline$ $5, 63, 73, 75, 79, 83, 89, 97$ $\newline$ 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, 63, 73, 75, 79, 83, 89, 97

\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: $5, 63, 73, 75, 79, 83, 89, 97$ . To find the outlier, we can look for a number that is significantly different from the rest of the data. In this case, $5$ is much lower than all other numbers, which are all above $60$ .
Calculate Mean with Outlier: Calculate the mean of the data set with the outlier included: $(5 + 63 + 73 + 75 + 79 + 83 + 89 + 97) / 8$ . Perform the addition: $5 + 63 + 73 + 75 + 79 + 83 + 89 + 97 = 564$ . Now divide by $8$ : $564 / 8 = 70.5$ . The mean with the outlier is $70.5$ .
Calculate Mean without Outlier: Calculate the mean of the data set without the outlier: $(63 + 73 + 75 + 79 + 83 + 89 + 97) / 7$ . Perform the addition: $63 + 73 + 75 + 79 + 83 + 89 + 97 = 559$ . Now divide by $7$ : $559 / 7 = 79.857$ . The mean without the outlier is approximately $79.857$ .
Compare Means: Compare the two means to determine if the mean would increase or decrease upon the removal of the outlier. The mean with the outlier is $70.5$ , and the mean without the outlier is approximately $79.857$ . Since $79.857$ is greater than $70.5$ , the mean would increase if the outlier were removed.

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