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Select the outlier in the data set. $\newline$ $26, 36, 38, 49, 57, 59, 60, 78, 596$ $\newline$ 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

26, 36, 38, 49, 57, 59, 60, 78, 596

\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: Step $1$ : Identify the outlier in the data set. $\newline$ Data set: $26, 36, 38, 49, 57, 59, 60, 78, 596$ $\newline$ To find the outlier, look for a number that is significantly different from the rest. Here, $596$ stands out as it is much higher than the other numbers.
Calculate Mean with Outlier: Step $2$ : Calculate the mean of the data set including the outlier. $\newline$ Mean = $(26 + 36 + 38 + 49 + 57 + 59 + 60 + 78 + 596) / 9$ $\newline$ Mean = $999 / 9$ $\newline$ Mean = $111$
Calculate Mean without Outlier: Step $3$ : Calculate the mean of the data set without the outlier. $\newline$ Mean without outlier = $(26 + 36 + 38 + 49 + 57 + 59 + 60 + 78) / 8$ $\newline$ Mean without outlier = $403 / 8$ $\newline$ Mean without outlier = $50.375$
Compare Mean Changes: Step $4$ : Compare the two means to determine if the mean increases or decreases when the outlier is removed. $\newline$ Original mean = $111$ $\newline$ Mean without outlier = $50.375$ $\newline$ Since $50.375$ is less than $111$ , removing the outlier decreases the mean.

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