Select the outlier in the data set. $\newline$ $2, 73, 77, 78, 79, 82, 84, 88, 98$ $\newline$ 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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Algebra 1

Identify an outlier and describe the effect of removing it

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Q. Select the outlier in the data set.

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2, 73, 77, 78, 79, 82, 84, 88, 98

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

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Choices:

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(A)increase

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(B)decrease

Identify Outlier: Identify the outlier in the data set. $\newline$ To find the outlier, we can look for a number that is significantly different from the rest of the numbers in the set. In this case, the number $2$ stands out as being much lower than all other numbers, which are all $73$ or higher.
Determine Outlier Using IQR: Determine if $2$ is an outlier using the interquartile range (IQR) method. $\newline$ First, we need to find the first quartile ( $Q1$ ) and the third quartile ( $Q3$ ) of the data set. Since there are $9$ numbers, the middle number is the median, which is $79$ . The lower half of the data set is $2, 73, 77, 78$ , and the upper half is $82, 84, 88, 98$ . The median of the lower half is $75$ (the average of $73$ and $77$ ), and the median of the upper half is $Q1$ $0$ (the average of $Q1$ $1$ and $Q1$ $2$ ). Therefore, $Q1$ is $75$ and $Q3$ is $Q1$ $0$ . $\newline$ Next, calculate the IQR: $Q1$ $7$ . $\newline$ Now, calculate the lower bound for outliers: $Q1$ $8$ . $\newline$ Since $2$ is less than $Q3$ $0$ , it is an outlier.
Calculate Mean with Outlier: Calculate the mean of the data set with and without the outlier. $\newline$ First, calculate the mean with the outlier included: $\newline$ Mean = $(2 + 73 + 77 + 78 + 79 + 82 + 84 + 88 + 98) / 9$ $\newline$ Mean = $661 / 9$ $\newline$ Mean $\approx 73.44$ $\newline$ Next, calculate the mean without the outlier: $\newline$ Mean = $(73 + 77 + 78 + 79 + 82 + 84 + 88 + 98) / 8$ $\newline$ Mean = $659 / 8$ $\newline$ Mean $\approx 82.38$
Determine Mean Change: Determine if the mean would increase or decrease without the outlier. Comparing the two means calculated in Step $3$ , we see that the mean without the outlier ( $82.38$ ) is higher than the mean with the outlier ( $73.44$ ). Therefore, removing the outlier would increase the mean.