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Select the outlier in the data set.
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Q. Select the outlier in the data set.
- Identify Outlier: Data set: To find the outlier, we need to look for a number that is significantly different from the rest of the numbers in the set.
- Calculate Median: First, let's calculate the median of the data set to understand the central tendency. The median is the middle value when the numbers are arranged in order. Since there are numbers, the median will be the average of the th and th numbers after arranging the data set in ascending order. The data set is already in ascending order, so the median is
- Calculate Quartiles: Next, we calculate the first quartile () and the third quartile (). These are the medians of the first half and the second half of the data set, respectively.For , we take the median of the first four numbers: For , we take the median of the last four numbers:
- Calculate IQR: Now, we calculate the interquartile range (IQR), which is .
- Find Bounds: To identify outliers, we can use the IQR to find the bounds outside of which a number is considered an outlier. The lower bound is , and the upper bound is . Lower bound = Upper bound =
- Identify Outlier: Any number in the data set that is lower than the lower bound or higher than the upper bound is considered an outlier.In our data set, the number is below the lower bound of .Therefore, is the outlier in the data set.
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