Select the outlier in the data set. $\newline$ $4, 58, 60, 61, 62, 64, 65, 67, 72$ $\newline$ 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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Grade 8

Identify an outlier and describe the effect of removing it

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Q. Select the outlier in the data set.

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4, 58, 60, 61, 62, 64, 65, 67, 72

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

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Choices:

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(A)increase

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(B)decrease

Identify Outlier: Identify the outlier in the given data set. $\newline$ The data set is: $4, 58, 60, 61, 62, 64, 65, 67, 72$ . $\newline$ An outlier is a value that is significantly higher or lower than most of the other values in a data set. To identify an outlier, we can use the interquartile range (IQR) method or simply look for a value that is distinctly separate from the cluster of other values. $\newline$ In this case, without calculating the IQR, we can see that the number $4$ is much lower than all the other numbers, which are all $58$ or higher. Therefore, $4$ is the outlier.
Calculate Mean with Outlier: Calculate the mean of the data set with the outlier included. $\newline$ To find the mean, add all the numbers together and then divide by the number of values. $\newline$ Mean = $(4 + 58 + 60 + 61 + 62 + 64 + 65 + 67 + 72) / 9$ $\newline$ Mean = $503 / 9$ $\newline$ Mean $\approx 55.89$
Calculate Mean without Outlier: Calculate the mean of the data set without the outlier. $\newline$ Remove the outlier $4$ and then calculate the new mean. $\newline$ New Mean = $(58 + 60 + 61 + 62 + 64 + 65 + 67 + 72) / 8$ $\newline$ New Mean = $509 / 8$ $\newline$ New Mean $\approx 63.63$
Compare Mean Changes: Compare the two means to determine if the mean would increase or decrease upon the removal of the outlier. The original mean with the outlier was approximately $55.89$ , and the new mean without the outlier is approximately $63.63$ . Since the new mean is higher than the original mean, the mean would increase if the outlier were removed.