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.

The shape does not matter when determining the appropriate measure of center.
The shape does not matter when determining the appropriate 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.

1 answer

The correct response is:

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

This is because, in a symmetrical distribution (such as a normal distribution), the mean is a good representation of the center of the data since it is centrally located and not affected by outliers. In contrast, if the data is skewed (either left or right), the mean can be pulled in the direction of the skew, making it less representative of the typical value. In such cases, the median is often preferred as it better reflects the center of the data by being less affected by outliers and the skewness. Therefore, the shape of the distribution is critical in determining which measure of center to use.