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Select the outlier in the data set.If the outlier were removed from the data set, would the mean increase or decrease?Choices:(A)increase(B)decrease
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Q. Select the outlier in the data set.If the outlier were removed from the data set, would the mean increase or decrease?Choices:(A)increase(B)decrease
- Identify Outlier: Identify the outlier in the data set.To find the outlier, we can look for a number that is significantly different from the rest of the numbers in the set. In this case, the number stands out as it is much larger than all other numbers.
- Determine Outlier: Determine if is an outlier using the interquartile range (IQR) method or by observing the gap between it and the other numbers.The gap between and the next highest number, , is very large. This suggests that is an outlier without doing a detailed IQR calculation.
- Calculate Mean with Outlier: Calculate the mean of the data set with the outlier included.Mean = Mean = Mean =
- Calculate Mean without Outlier: Calculate the mean of the data set without the outlier.Mean without outlier = Mean without outlier = Mean without outlier
- Compare Means: Compare the two means to determine if the mean would increase or decrease when the outlier is removed.The mean with the outlier is , and the mean without the outlier is approximately . Since the mean without the outlier is less than the mean with the outlier, removing the outlier would decrease the mean.
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