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Select the outlier in the data set. $\newline$ $15, 19, 31, 71, 72, 74, 87, 99, 524$ $\newline$ 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

15, 19, 31, 71, 72, 74, 87, 99, 524

\newline

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

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

Calculate Mean and Standard Deviation: Calculate the mean and standard deviation of the data set. $\newline$ Mean (average) = $(15 + 19 + 31 + 71 + 72 + 74 + 87 + 99 + 524) / 9$ $\newline$ Mean = $992 / 9$ $\newline$ Mean $\approx 110.22$
Calculate Standard Deviation: Calculate the standard deviation. $\newline$ To find the standard deviation, we need to calculate the variance first. This involves finding the squared differences from the mean, averaging those, and then taking the square root. However, for the purpose of identifying an outlier, we can use a simpler method by looking for a value that is significantly higher or lower than the rest. $\newline$ In this case, $524$ is much higher than all other values, which suggests it is the outlier.
Identify Outlier: Identify the outlier. $\newline$ An outlier is a value that is significantly higher or lower than the rest of the data. In this data set, $524$ stands out from the other values, which are all below $100$ . Therefore, $524$ is the outlier.
Effect of Removing Outlier: Determine the effect on the mean if the outlier is removed. $\newline$ Removing an outlier that is significantly higher than the mean will result in a decrease in the mean. Since $524$ is much higher than the current mean, removing it will decrease the mean.

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