Explain how the shape of a distribution determines the appropriate measure of center. (1 point) skewed data means that the mean is the best measure of center. Symmetrical data means that the mean is the best measure of center. The shape does not matter when determining the appropriate measure of center. More information is needed to determine how the data of distribution determines the appropriate measure of center.

The shape of a distribution significantly influences the choice of the appropriate measure of center (mean, median, or mode). Here's a breakdown of how different shapes affect this decision: 1. **Skewed Data**: - When a distribution is skewed (either to the left or right), the mean is affected by extreme values (outliers) and may not accurately represent the center of the data. In such cases, the median is often a better measure of center because it is less influenced by outliers and provides a better indication of the typical value in the dataset. 2. **Symmetrical Data**: - In a symmetrical distribution (like a normal distribution), the mean, median, and mode are all located at the same point. Therefore, the mean is a suitable measure of center because it accurately reflects the central tendency of the data without being skewed by outliers. 3. **Shape Does Matter**: - The shape of the distribution is crucial when determining the appropriate measure of center. Using the mean for skewed data can lead to misleading conclusions, while using the median for symmetrical data may not provide any additional benefit. 4. **More Information Needed**: - While the shape provides a strong guideline, additional context about the data (such as the presence of outliers or the specific research question) may also influence the choice of the measure of center. In summary, the correct statement is that the shape of the distribution does matter when determining the appropriate measure of center. Specifically, skewed data typically suggests using the median, while symmetrical data supports the use of the mean.