How does the outlier affect the mean?
Understand the Problem
The question is asking about the impact of outliers on the mean value of a data set. An outlier is a data point that differs significantly from other observations. It seeks to understand how these extreme values influence the overall average (mean) of a group of numbers.
Answer
Outliers affect the mean by pulling it towards their extreme values.
The final answer is Outliers affect the mean by pulling it towards their extreme values, making it either larger or smaller, while having little effect on the median.
Answer for screen readers
The final answer is Outliers affect the mean by pulling it towards their extreme values, making it either larger or smaller, while having little effect on the median.
More Information
The mean is sensitive to outliers because it takes all values into account, so extreme values can significantly alter the average. Other measures of central tendency like the median are less affected because they consider only the position of data points in the ordered list.
Tips
A common mistake is to use the mean for datasets with outliers without considering its sensitivity. Instead, the median might be more appropriate in such cases.
Sources
- How do outliers influence measures of central tendency and dispersion? - ck12.org
- How does an outlier affect the mean of a data set? - Socratic - socratic.org
- How Do Outliers Affect the Mean? - Statology - statology.org
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