Question

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.

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.
Symmetrical 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.

1 answer

The appropriate measure of center is influenced by the shape of the data distribution. Specifically:

  • Skewed data: When a distribution is skewed (either left or right), the mean can be heavily influenced by outliers or extreme values, leading to a measure of center that may not accurately reflect the typical value of the data. In such cases, the median is often a better measure of center because it is not affected by those outliers.

  • Symmetrical data: When the distribution is symmetrical, the mean and median are generally very close or the same. In this scenario, the mean is typically considered the best measure of center because it takes into account all values in the dataset.

Thus, the correct response is that for symmetrical data, the mean is the best measure of center, while for skewed data, the median is more appropriate.