Question

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.

The shape does not matter when determining the appropriate 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.
More information is needed to determine how the data of distribution determines the appropriate measure of center.

Answer 1

The correct response is:

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

In more detail, when a distribution is symmetrical, the mean is a good measure of center because it accurately reflects the central tendency of the data. However, in skewed distributions, the mean can be influenced by extreme values (outliers), making the median a more appropriate measure of center, as it is less affected by those extremes. Therefore, the shape of the distribution is crucial in determining which measure (mean or median) best represents the center of the data.