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Select the outlier in the data set. $\newline$ $9, 65, 67, 69, 74, 77, 78, 86, 96$ $\newline$ 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

9, 65, 67, 69, 74, 77, 78, 86, 96

\newline

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

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $9$ , $65$ , $67$ , $69$ , $74$ , $77$ , $78$ , $86$ , $96$ .
Calculate Median: Calculate the median of the data set. $\newline$ The middle term of the given data set is $74$ . $\newline$ Median: $74$
Calculate Quartiles: Calculate the first and third quartiles ( $Q1$ and $Q3$ ). $\newline$ The lower half of the data set for $Q1$ is $9$ , $65$ , $67$ , $69$ . $\newline$ The median of this lower half is the average of $65$ and $67$ . $\newline$ $Q1$ : $Q3$ $0$ $\newline$ The upper half of the data set for $Q3$ is $Q3$ $2$ , $Q3$ $3$ , $Q3$ $4$ , $Q3$ $5$ . $\newline$ The median of this upper half is the average of $Q3$ $3$ and $Q3$ $4$ . $\newline$ $Q3$ : $Q3$ $9$
Calculate IQR: Calculate the interquartile range (IQR). $IQR = Q3 - Q1 = 82 - 66 = 16$
Determine Outlier Boundaries: Determine the outlier boundaries. $\newline$ Lower boundary = $Q1 - 1.5 \times IQR = 66 - 1.5 \times 16 = 66 - 24 = 42$ $\newline$ Upper boundary = $Q3 + 1.5 \times IQR = 82 + 1.5 \times 16 = 82 + 24 = 106$
Identify Outlier: Identify the outlier(s). $\newline$ The value $9$ is below the lower boundary of $42$ , so it is an outlier. $\newline$ Outlier: $9$
Effect on Mean: Determine the effect of removing the outlier on the mean. $\newline$ Removing a value that is lower than the mean will increase the overall mean of the data set.

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