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Select the outlier in the data set. $\newline$ $45, 55, 65, 75, 85, 87, 95, 392$

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Geometric sequences

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Q. Select the outlier in the data set.

\newline

45, 55, 65, 75, 85, 87, 95, 392

Observe Data Set: Arrange the data set in ascending order and observe the values. $\newline$ The data set is already in ascending order: $45, 55, 65, 75, 85, 87, 95, 392$ . $\newline$ Looking at the data set, we can see that the number $392$ stands out as it is much larger than the rest of the numbers.
Calculate Differences: Calculate the difference between consecutive numbers to see if one difference is significantly larger than the others. $\newline$ $45$ to $55$ : $55 - 45 = 10$ $\newline$ $55$ to $65$ : $65 - 55 = 10$ $\newline$ $65$ to $75$ : $75 - 65 = 10$ $\newline$ $75$ to $55$ $0$ : $55$ $1$ $\newline$ $55$ $0$ to $55$ $3$ : $55$ $4$ $\newline$ $55$ $3$ to $55$ $6$ : $55$ $7$ $\newline$ $55$ $6$ to $55$ $9$ : $55 - 45 = 10$ $0$ $\newline$ The difference of $55 - 45 = 10$ $1$ is significantly larger than all other differences, indicating that $55$ $9$ is likely the outlier.
Confirm Outlier: Confirm that $392$ is an outlier by comparing it to the rest of the data set. All other numbers are within $10$ units of their adjacent numbers, while $392$ is $297$ units away from the nearest number. This confirms that $392$ is an outlier.

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