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Select the outlier in the data set. $\newline$ $75, 77, 79, 81, 82, 85, 87, 423$ $\newline$ 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

75, 77, 79, 81, 82, 85, 87, 423

\newline

If the outlier were removed from the data set, would the mean increase or decrease?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

Understand Mean Concept: Now, let's think about what happens to the mean if we take out the outlier. The mean is like the average, right? So if we take out a really big number from a bunch of smaller numbers, the average is gonna go down.
Calculate Mean with Outlier: To be super sure, let's calculate the mean with and without the outlier. First, with the outlier: add all the numbers up and divide by how many there are. So, $75 + 77 + 79 + 81 + 82 + 85 + 87 + 423$ equals... umm, let's see... $989$ . There are $8$ numbers, so $989$ divided by $8$ is about $123.625$ .
Calculate Mean without Outlier: Now, let's do it without the $423$ . Add up the remaining numbers: $75 + 77 + 79 + 81 + 82 + 85 + 87$ equals $566$ . There are $7$ numbers now, so $566$ divided by $7$ is... $80.857$ . Yeah, that's definitely lower than $123.625$ .
Compare Mean Values: So, removing the outlier, which is $423$ , makes the mean decrease. The answer to the question is (B) decrease.

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