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Select the outlier in the data set. $\newline$ $37, 44, 48, 49, 50, 51, 55, 709$ $\newline$ 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

37, 44, 48, 49, 50, 51, 55, 709

\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 looking for a number that is significantly different from the rest of the data. $\newline$ Looking at the data set: $37, 44, 48, 49, 50, 51, 55, 709$ , it's clear that $709$ is way higher than all other numbers.
Confirm Outlier: Confirm that $709$ is the outlier by comparing it to the rest of the data set. $\newline$ All other numbers are within a range of $37$ to $55$ , so $709$ is the outlier.
Calculate Mean with Outlier: Calculate the mean of the original data set with the outlier. $\newline$ Mean = $(37 + 44 + 48 + 49 + 50 + 51 + 55 + 709) / 8$ $\newline$ Mean = $993 / 8$ $\newline$ Mean = $124.125$
Calculate Mean without Outlier: Calculate the mean of the data set without the outlier. $\newline$ Mean without outlier = $(37 + 44 + 48 + 49 + 50 + 51 + 55) / 7$ $\newline$ Mean without outlier = $334 / 7$ $\newline$ Mean without outlier = $47.714285714285715$
Compare Means: Compare the two means to determine if the mean would increase or decrease after removing the outlier. Since $124.125$ (with outlier) is greater than $47.714285714285715$ (without outlier), removing the outlier will decrease the mean.

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