Explain how the shape of a distribution determines the appropriate measure of center.(1 point)

Question

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 correct response is:

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

In a symmetrical distribution, the values are evenly distributed around the center, which allows the mean to accurately represent the central tendency of the data. Conversely, in a skewed distribution (where data points cluster on one side of the distribution), the mean can be disproportionately affected by extreme values, making the median a more appropriate measure of center. Therefore, the shape of the distribution is key in determining which measure of center (mean or median) is most appropriate.