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Select the outlier in the data set. $\newline$ $11, 18, 20, 21, 22, 23, 25, 226$ $\newline$ 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

11, 18, 20, 21, 22, 23, 25, 226

\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: $11, 18, 20, 21, 22, 23, 25, 226$ $\newline$ Looking at the numbers, $226$ stands out as it is much higher than the rest of the values.
Calculate Mean Original: Step $2$ : Calculate the mean of the original data set. $\newline$ Mean = $(11 + 18 + 20 + 21 + 22 + 23 + 25 + 226) / 8$ $\newline$ Mean = $366 / 8$ $\newline$ Mean = $45.75$
Calculate Mean Without Outlier: Step $3$ : Calculate the mean of the data set without the outlier. $\newline$ New data set without $226$ : $11, 18, 20, 21, 22, 23, 25$ $\newline$ Mean = $(11 + 18 + 20 + 21 + 22 + 23 + 25) / 7$ $\newline$ Mean = $140 / 7$ $\newline$ Mean = $20$
Compare Means: Step $4$ : Compare the two means to determine if the mean increases or decreases after removing the outlier. $\newline$ Original mean: $45.75$ $\newline$ New mean without outlier: $20$ $\newline$ Since $20$ is less than $45.75$ , removing the outlier decreases the mean.

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