Which measures of center are influenced by outliers?

Select all that apply.

Group of answer choices

mode

mean

midrange

median

The measures of center that are influenced by outliers are:

- **Mean**
- **Midrange**

### Explanation:
- **Mean**: The mean is highly sensitive to outliers because it involves adding up all the values and dividing by the number of values. An extreme value can significantly shift the mean.
  
- **Midrange**: The midrange is calculated as the average of the maximum and minimum values in the dataset. Since it directly involves the extreme values, it is also highly sensitive to outliers.

### Not Influenced by Outliers:
- **Median**: The median is the middle value in a sorted dataset and is not influenced by outliers, as it depends only on the position, not the magnitude, of values.
  
- **Mode**: The mode is the most frequent value in the dataset and is not influenced by outliers.

### Correct Answers: **Mean** and **Midrange**

Would you like more details or have any questions about this? Here are some related questions to explore further:

1. Why is the median often preferred over the mean in skewed distributions?
2. How does the presence of outliers affect the interpretation of the mean?
3. In what situations might the midrange be a useful measure of center despite its sensitivity to outliers?
4. How can outliers be detected and handled in a dataset?
5. What are some real-life examples where the mean is misleading due to outliers?

**Tip:** When dealing with data that may have outliers, consider using the median or mode as a more robust measure of center.

Explore how measures of center such as mean and midrange are influenced by outliers in statistical analysis. Learn why these measures are sensitive to extreme values and how they differ from the median and mode. Suitable for students and researchers interested in statistical data analysis.

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