The histogram shown represents the distribution of salaries, in thousands of dollars, for 28 players on a professional soccer team. Which of the following explains whether the mean or the median of the data is the more reasonable estimate of the typical salary of a player on the team?

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Since the distribution is symmetric, the mean and the median are equally accurate estimates of the typical salary.

The median is a more accurate estimate of the typical salary than the mean because it is not as affected by outliers.

Since the distribution is skewed, neither the mean nor the median can be used to estimate the typical salary.

The mean is a more accurate estimate of the typical salary than the median because it is not as affected by outliers.

The correct answer is:

**The median is a more accurate estimate of the typical salary than the mean because it is not as affected by outliers.**

### Explanation:

- **Symmetric Distribution**: If the distribution of the salaries were symmetric (like a bell curve), the mean and median would be close, making both good estimates for the typical salary. However, we don't have that information.

- **Skewed Distribution**: If the histogram shows a skewed distribution (especially if it is right-skewed with a long tail of higher salaries), the mean would be higher than the median because the mean is affected by the high salaries (outliers). In this case, the median is a better representation of the typical salary since it is less influenced by outliers.

- **Outliers Impact**: The mean is sensitive to extreme values (outliers), which can pull the mean in their direction, making it less representative of the central tendency for most players. The median, being the middle value, is not affected by the magnitude of outliers, thus providing a better estimate of the typical salary.

Since we often expect salaries to be right-skewed (a few players earning much more than others), the median is typically more representative of the typical salary.

### Would you like more details on this explanation or have any other questions?

Here are 5 related questions:
1. What is the difference between mean, median, and mode?
2. How do you calculate the median in a dataset?
3. What are the common characteristics of a right-skewed distribution?
4. How does the presence of outliers affect the mean in a dataset?
5. Can you provide an example where the mean is more representative than the median?

**Tip:** When analyzing data, always look at the distribution shape before choosing the best measure of central tendency (mean, median, or mode).

Understand the difference between mean and median in statistics for estimating typical salary based on a professional soccer team's salary distribution. Learn why the median is often a more accurate estimate due to its resistance to outliers.

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