Effect of Outliers on the Mean
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Data set A
Data set B
The two histograms show the distribution of data set A and data set B, respectively. Data set B is the result of removing the outlier from data set A. Which of the following statements about the means of data set A and data set B is true?
A) The means of data set A and B are the same.
B) The mean of data set A is greater than the mean of data set B.
C) The mean of data set A is less than the mean of data set B.
D) No comparison about the means of the data sets can be made.
This question includes visual content: Two histograms labeled 'Data set A' and 'Data set B'. Both have a horizontal axis ranging from 0 to 70 with increments of 10, and a vertical axis labeled 'Frequency' ranging from 0 to 5. Data set A contains bars with frequencies: [0-10]: 2, [10-20]: 5, [20-30]: 3, [30-40]: 2, and [60-70]: 1. Data set B contains the exact same bars except for the [60-70] interval, which has a frequency of 0, indicating the removal of the outlier.
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Let's compare the means of two data sets represented by these histograms. We're told that data set B is created by removing the outlier from data set A.
Effect of Outliers on the Mean
Let's first identify that outlier in data set A. Notice that there is a single data point in the range of sixty to seventy, which is significantly higher than the rest of the data clustered between zero and forty.
Recall the formula for the mean: it is the sum of all values divided by the total number of values.
An outlier on the high end of a distribution adds a significantly large value to the sum. Since the mean is highly sensitive to extreme values, this pulls the mean of data set A toward the right.
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