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Select the outlier in the data set. $\newline$ $42, 52, 60, 64, 65, 68, 72, 78, 678$ $\newline$ 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

42, 52, 60, 64, 65, 68, 72, 78, 678

\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 the outlier: Step $1$ : Identify the outlier in the data set. $\newline$ Data set: $42, 52, 60, 64, 65, 68, 72, 78, 678$ $\newline$ To find the outlier, look for a number that is significantly different from the rest. Here, $678$ 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 = $\frac{42 + 52 + 60 + 64 + 65 + 68 + 72 + 78 + 678}{9}$ $\newline$ Mean = $\frac{1229}{9}$ $\newline$ Mean = $136$ . $56$
Calculate mean without outlier: Step $3$ : Calculate the mean of the data set without the outlier. $\newline$ Mean without outlier = $(42 + 52 + 60 + 64 + 65 + 68 + 72 + 78) / 8$ $\newline$ Mean without outlier = $501 / 8$ $\newline$ Mean without outlier = $62.625$
Compare mean with and without outlier: Step $4$ : Compare the two means to determine if the mean increases or decreases when the outlier is removed. $\newline$ Mean with outlier = $136.56$ $\newline$ Mean without outlier = $62.625$ $\newline$ Since the mean without the outlier is less than the mean with the outlier, removing the outlier decreases the mean.

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