Question

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

Answer 1

The shape of a distribution significantly influences which measure of center—mean, median, or mode—is most appropriate. In general:

• Symmetrical data: When a distribution is symmetrical (bell-shaped), the mean is the best measure of center because it accurately reflects the central tendency of the data. In symmetrical distributions, the mean, median, and mode are all approximately equal.

• Skewed data: For data that is skewed (either positively or negatively), the mean can be influenced by outliers or extreme values, which can distort the representation of the center. In such cases, the median is often preferred as it provides a better measure of center by representing the middle of the data without being affected by extreme values.

Based on this understanding, the correct response would be that the shape of the distribution determines the appropriate measure of center, specifically:

• Symmetrical data means that the mean is the best measure of center.
• Skewed data means that the median is the best measure of center.