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

Answer 1

The appropriate measure of center in a distribution is significantly influenced by its shape. Here's a brief explanation of the key concepts:

1. Symmetrical Distribution: In a symmetrical distribution (like a normal distribution), the mean, median, and mode are all located near the center and have similar values. Therefore, the mean is often considered the best measure of center because it takes into account all values and provides a balanced measure.

2. Skewed Distribution: In a skewed distribution (either positively or negatively skewed), the mean is pulled in the direction of the skew, which can result in a misleading representation of the center. In such cases, the median is a better measure of center because it is less affected by extreme values (outliers) and represents the middle value of the data more accurately.

3. When to use each:

   • Use the mean for symmetrical distributions, as it provides a useful summary of the data.
   • Use the median for skewed distributions to better represent the central tendency without being distorted by outliers.

In summary, the shape of the data distribution is crucial in determining whether the mean or median is a more appropriate measure of center, making the statement "Symmetrical data means that the mean is the best measure of center" the accurate response.