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Select the outlier in the data set. $\newline$ $64, 69, 71, 72, 73, 74, 76, 156$ $\newline$ 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

64, 69, 71, 72, 73, 74, 76, 156

\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: $64, 69, 71, 72, 73, 74, 76, 156$ . An outlier is a data point that is significantly different from the rest of the data. We can visually inspect the data set and see that $156$ is much larger than all other numbers, which are relatively close to each other.
Confirm Outlier: To confirm that $156$ is an outlier, we can calculate the interquartile range (IQR) and then determine the upper bound above which a data point would be considered an outlier. However, since $156$ is clearly much larger than the rest, we can proceed without this calculation.
Calculate Mean with Outlier: Calculate the mean of the data set with the outlier included: $(64 + 69 + 71 + 72 + 73 + 74 + 76 + 156) / 8$ . Perform the calculation: $645 / 8 = 80.625$ .
Calculate Mean without Outlier: Calculate the mean of the data set without the outlier: $(64 + 69 + 71 + 72 + 73 + 74 + 76) / 7$ . Perform the calculation: $499 / 7 = 71.2857$ .
Compare Means: Compare the two means: with the outlier, the mean is $80.625$ ; without the outlier, the mean is $71.2857$ . Since the mean without the outlier is less than the mean with the outlier, removing the outlier would decrease the mean.

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