A data set has a mean of
and a median of
. Would you expect this data set to be skewed to the right, skewed to the left, or approximately symmetric?

To determine the skewness of a data set based on its mean and median:

- **Right Skewed (Positively Skewed)**: If the mean is greater than the median, the data is likely skewed to the right. This occurs because the higher values pull the mean up more than they affect the median.

- **Left Skewed (Negatively Skewed)**: If the mean is less than the median, the data is likely skewed to the left. This occurs because the lower values pull the mean down more than they affect the median.

- **Approximately Symmetric**: If the mean is approximately equal to the median, the data is likely symmetric, meaning the distribution is roughly the same on both sides.

Since the specific values of the mean and median are not provided, here's a general guideline:

- **If the mean > median**: The data set is likely **skewed to the right**.
- **If the mean < median**: The data set is likely **skewed to the left**.
- **If the mean ≈ median**: The data set is likely **approximately symmetric**.

Would you like to know more details about skewness, or do you have any questions?

Here are 5 related questions:
1. How does skewness affect the interpretation of a data set?
2. What are some common examples of right-skewed and left-skewed distributions?
3. How can you calculate skewness using statistical software?
4. What is the relationship between skewness and the shape of a histogram?
5. How do outliers impact the skewness of a data set?

**Tip:** When analyzing data, always consider both the mean and median together to gain insights into the distribution's shape.

Explore how mean and median determine the skewness of a dataset in statistics. Learn the concepts of right skew, left skew, and symmetric distributions with practical examples. Suitable for Grades 9-12.

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