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Select the outlier in the data set. $\newline$ $78, 84, 86, 87, 88, 89, 93, 218$ $\newline$ 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

78, 84, 86, 87, 88, 89, 93, 218

\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 in the given data set: $78, 84, 86, 87, 88, 89, 93, 218$ . To find the outlier, we can look for a number that is significantly different from the rest of the data.
Find Outlier: Looking at the data set, we can see that $218$ is much larger than all the other numbers, which are all below $100$ . Therefore, $218$ is the outlier.
Calculate Mean with Outlier: Now, let's calculate the mean of the data set with the outlier included. $\newline$ Mean with outlier = $\frac{78 + 84 + 86 + 87 + 88 + 89 + 93 + 218}{8}$ $\newline$ Mean with outlier = $\frac{823}{8}$ $\newline$ Mean with outlier = $102.875$
Calculate Mean without Outlier: Next, calculate the mean of the data set without the outlier. $\newline$ Mean without outlier = $(78 + 84 + 86 + 87 + 88 + 89 + 93) / 7$ $\newline$ Mean without outlier = $605 / 7$ $\newline$ Mean without outlier = $86.4286$
Compare Means: Compare the two means to determine if the mean would increase or decrease with the removal of the outlier. Since $102.875$ (with outlier) is greater than $86.4286$ (without outlier), removing the outlier will decrease the mean.

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