https://file.aiquickdraw.com/mathbot/file/1726054069573oaeo1plx.jpg

The statistics from the image show the effects of an outlier on different measures of central tendency and spread.

1. **Median**: The median remains unchanged at 5 when the 8 is replaced by 800. This is because the median is the middle value in an ordered list, and changing one value far beyond the others does not affect the position of the median in small datasets.

2. **Mean**: The mean increases significantly from 5.2 to 163.6 due to the influence of the outlier. The mean is sensitive to outliers because it is the average of all values in the dataset.

3. **Standard Deviation**: The standard deviation also remains nearly unchanged at 2.14, which suggests that the initial computation or the influence of the outlier might not have been accurately represented in this context. Typically, the standard deviation should increase when a large outlier is added, as it measures the average distance of data points from the mean.

From this, we can see that the **median** was the statistic least changed by the outlier of 800, affirming the answer provided in the image.

Do you have any further questions or need more details on this? Here are some related questions and topics you might find interesting:
1. What happens to the variance in the presence of an outlier?
2. How does the median change if the number of observations is even?
3. Why is the mean more sensitive to outliers than the median?
4. Can replacing other numbers with different outliers affect the mean differently?
5. What is the impact of outliers on data interpretation in statistical analyses?

Tip: When analyzing data sets, always consider the impact of outliers on your calculations, as they can significantly skew the results.

Sometimes outliers can have a significant effect on statistics, and sometimes they don't. Use the following distribution to determine which statistics are affected by outliers. Round to the nearest hundredth. Data: 2, 4, 5, 7, 8.

Analyze how outliers affect the mean, median, and standard deviation of the data set 2, 4, 5, 7, 8. When 8 is replaced by 800, observe how the mean and standard deviation change, while the median remains the same. Learn key statistical concepts and their real-world implications.

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