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Select the outlier in the data set. $\newline$ $70, 80, 82, 83, 84, 85, 89, 91, 812$ $\newline$ 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

70, 80, 82, 83, 84, 85, 89, 91, 812

\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 $70, 80, 82, 83, 84, 85, 89, 91, 812$ . Outliers are numbers that are significantly different from the others in a data set. Here, $812$ stands out as it is much larger than the rest of the numbers.
Calculate Mean: Step $2$ : Calculate the mean of the original data set. $\newline$ Mean = $(70 + 80 + 82 + 83 + 84 + 85 + 89 + 91 + 812) / 9$ $\newline$ Mean = $1476 / 9$ $\newline$ Mean = $164$
Remove Outlier: Step $3$ : Remove the outlier $812$ and calculate the new mean. $\newline$ New Mean = $(70 + 80 + 82 + 83 + 84 + 85 + 89 + 91) / 8$ $\newline$ New Mean = $664 / 8$ $\newline$ New Mean = $83$
Compare Means: Step $4$ : Compare the original mean $164$ with the new mean $83$ to determine if the mean increased or decreased. $\newline$ Since $83$ is less than $164$ , removing the outlier decreased the mean.

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