The last 10 calls to a customer support line had the following lengths (in minutes).13, 52, 52, 55, 59, 60, 62, 63, 64, 99Identify all values that are outliers.If there is more than one outlier, separate them with commas.If there are no outliers, click on "None". None
Question
The last 10 calls to a customer support line had the following lengths (in minutes).13, 52, 52, 55, 59, 60, 62, 63, 64, 99Identify all values that are outliers.If there is more than one outlier, separate them with commas.If there are no outliers, click on "None". None
Solution
To identify outliers in a data set, we typically use the Interquartile Range (IQR) method. Here are the steps:
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First, we need to sort the data in ascending order: 13, 52, 52, 55, 59, 60, 62, 63, 64, 99.
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Then, we find the first quartile (Q1), which is the median of the first half of the data. In this case, since we have 10 data points, the first half is the first 5 numbers: 13, 52, 52, 55, 59. The median of these numbers is 52.
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Next, we find the third quartile (Q3), which is the median of the second half of the data. The second half of the data is: 60, 62, 63, 64, 99. The median of these numbers is 63.
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Now, we calculate the interquartile range (IQR), which is Q3 - Q1 = 63 - 52 = 11.
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We find the lower bound for outliers, which is Q1 - 1.5IQR = 52 - 1.511 = 36.5. Any number less than this is considered an outlier.
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We find the upper bound for outliers, which is Q3 + 1.5IQR = 63 + 1.511 = 78.5. Any number greater than this is considered an outlier.
Looking at our data set, we see that 13 and 99 are outliers because they are less than 36.5 and greater than 78.5, respectively. So, the outliers are 13 and 99.
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