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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 lower 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 closest number in the set.The gap between and the next closest number, , is , which is significantly larger than the gaps between any other two consecutive numbers in the set. This suggests that is indeed an outlier.
- Calculate Mean: Calculate the mean of the original data set.Mean = Mean = Mean =
- Remove Outlier: Remove the outlier and calculate the new mean of the remaining data set.New Mean New Mean New Mean
- Compare Means: Compare the original mean to the new mean to determine if it would increase or decrease.The original mean was , and the new mean without the outlier is . Since the new mean is higher, removing the outlier would increase the mean.
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