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Select the outlier in the data set.\newline75,77,79,81,82,85,87,42375, 77, 79, 81, 82, 85, 87, 423\newlineIf the outlier were removed from the data set, would the mean increase or decrease?\newlineChoices:\newline(A)increase\newline(B)decrease

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Full solution

Q. Select the outlier in the data set.\newline75,77,79,81,82,85,87,42375, 77, 79, 81, 82, 85, 87, 423\newlineIf the outlier were removed from the data set, would the mean increase or decrease?\newlineChoices:\newline(A)increase\newline(B)decrease
  1. 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.
  2. 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+42375 + 77 + 79 + 81 + 82 + 85 + 87 + 423 equals... umm, let's see... 989989. There are 88 numbers, so 989989 divided by 88 is about 123.625123.625.
  3. Calculate Mean without Outlier: Now, let's do it without the 423423. Add up the remaining numbers: 75+77+79+81+82+85+8775 + 77 + 79 + 81 + 82 + 85 + 87 equals 566566. There are 77 numbers now, so 566566 divided by 77 is... 80.85780.857. Yeah, that's definitely lower than 123.625123.625.
  4. Compare Mean Values: So, removing the outlier, which is 423423, makes the mean decrease. The answer to the question is (B) decrease.

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