Select the outlier in the data set. $\newline$ $76, 83, 87, 89, 94, 96, 98, 620$ $\newline$ 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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76, 83, 87, 89, 94, 96, 98, 620

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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 look for a number that is significantly different from the rest of the numbers in the data set. The numbers are $76$ , $83$ , $87$ , $89$ , $94$ , $96$ , $98$ , $620$ . It is clear that $620$ is much larger than all other numbers, which are all below $100$ .
Determine Outlier: Determine if $620$ is an outlier. An outlier is a value that is significantly higher or lower than the other values in a data set. In this case, $620$ is much higher than the rest of the values, which are all clustered below $100$ . Therefore, $620$ is the outlier.
Calculate Mean with Outlier: Calculate the mean of the data set with the outlier. $\newline$ To find the mean, add all the numbers together and divide by the number of values. The sum of the numbers is $76 + 83 + 87 + 89 + 94 + 96 + 98 + 620 = 1243$ . There are $8$ numbers in total. $\newline$ Mean with outlier = $\frac{1243}{8} = 155.375$
Calculate Mean without Outlier: Calculate the mean of the data set without the outlier. $\newline$ To find the new mean, subtract the outlier from the sum of the data set and divide by the new number of values $7$ instead of $8$ . The new sum is $1243 - 620 = 623$ . $\newline$ Mean without outlier = $\frac{623}{7} \approx 88.99$
Compare Means: Compare the means to determine if the mean would increase or decrease. $\newline$ The original mean with the outlier was $155.375$ , and the mean without the outlier is approximately $88.99$ . Since the mean without the outlier is less than the mean with the outlier, removing the outlier would decrease the mean.