Question

Question

For which distributions is the median the best measure of center?




Select each correct answer.



Responses

A bar graph that forms the shape of a pyramid on a graph.
Image with alt text: A bar graph that forms the shape of a pyramid on a graph.

A bar graph that forms a gradual incline and a sharp decline of values.
Image with alt text: A bar graph that forms a gradual incline and a sharp decline of values.

A bar graph that forms a sharp incline and a gradual decline of values.
Image with alt text: A bar graph that forms a sharp incline and a gradual decline of values.

A bar graph with values that hover around 10 y.

Answer 1

Answer: The median is the best measure of center for distributions that are skewed or have extreme values, since it is less affected by outliers than the mean. Therefore, the correct answers are:

- A bar graph that forms a gradual incline and a sharp decline of values.

- A bar graph that forms a sharp incline and a gradual decline of values.

Both of these graphs suggest that the data is skewed, and in these cases, the median is a better representation of the "typical" value than the mean.

The other two options do not provide enough information to determine whether the data is skewed or not, so we cannot say for certain whether the median is the best measure of center in those cases. The bar graph with values that hover around 10 y could have a symmetrical distribution with a mean and median that are the same, or it could have a skewed distribution where the median is a better measure of center. Similarly, the pyramid-shaped bar graph could have a symmetrical distribution, or it could be skewed in a way that the median is not a good measure of center.

Explanation: