Select the outlier in the data set. $\newline$ $6, 48, 54, 57, 58, 60, 62, 72$ $\newline$ 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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6, 48, 54, 57, 58, 60, 62, 72

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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 the 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 data set. The data set is: $6, 48, 54, 57, 58, 60, 62, 72$ . At first glance, the number $6$ stands out as being much lower than the rest of the numbers.
Confirm outlier comparison: Confirm the outlier by comparing it to the rest of the data. We can calculate the range and see if $6$ falls far outside the typical range of the data. The next lowest number is $48$ , and the highest is $72$ . The range of the rest of the data (excluding $6$ ) is from $48$ to $72$ , which is a range of $24$ . The number $6$ is $42$ units away from the next closest number, which is a significant difference compared to the range of the other numbers. This confirms that $6$ is an outlier.
Calculate mean with outlier: Calculate the mean of the data set with the outlier included. $\newline$ To find the mean, we add up all the numbers and divide by the total count. The sum of the data set is $6 + 48 + 54 + 57 + 58 + 60 + 62 + 72 = 417$ . The total count is $8$ . So, the mean is $417 / 8 = 52.125$ .
Calculate mean without outlier: Calculate the mean of the data set without the outlier. $\newline$ Now we remove the outlier $6$ and calculate the new mean. The new sum is $417 - 6 = 411$ . The new total count is $8 - 1 = 7$ . So, the new mean is $\frac{411}{7} \approx 58.714$ .
Determine mean change: Determine if the mean will increase or decrease after removing the outlier. Comparing the original mean $52.125$ with the new mean $58.714$ , we can see that the mean has increased after removing the outlier.