Question

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



Select each correct answer.

Responses

A bar graph with bars that gradually rises up to over 28 y then drop down to just above 10 y.
Image with alt text: A bar graph with bars that gradually rises up to over 28 y then drop down to just above 10 y.

A bar graph that forms a pyramid of bars, the vertex of which is 35 y.
Image with alt text: A bar graph that forms a pyramid of bars, the vertex of which is 35 y.

A bar graph with a majority of values measured above 4 y.
Image with alt text: A bar graph with a majority of values measured above 4 y.

A bar graph that steeply rises to 30 y then steeply drops to values above 2 y.
Image with alt text: A bar graph that steeply rises to 30 y then steeply drops to values above 2 y.







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



Select each correct answer.

Responses

A bar graph with bars that gradually rises up to over 28 y then drop down to just above 10 y.
Image with alt text: A bar graph with bars that gradually rises up to over 28 y then drop down to just above 10 y.

A bar graph that forms a pyramid of bars, the vertex of which is 35 y.
Image with alt text: A bar graph that forms a pyramid of bars, the vertex of which is 35 y.

A bar graph with a majority of values measured above 4 y.
Image with alt text: A bar graph with a majority of values measured above 4 y.

A bar graph that steeply rises to 30 y then steeply drops to values above 2 y.
Image with alt text: A bar graph that steeply rises to 30 y then steeply drops to values above 2 y.

Answer 1

The median is the best measure of center for distributions that are skewed or those that contain outliers. Here’s how you can evaluate the given options in terms of whether the median would be a suitable measure of center:

1. **A bar graph with bars that gradually rises up to over 28 y then drop down to just above 10 y.**
- This distribution appears to be skewed (possibly right-skewed) due to the drop after reaching a higher value. The median would be a better measure of center than the mean here.

2. **A bar graph that forms a pyramid of bars, the vertex of which is 35 y.**
- This likely indicates a symmetrical distribution (like a normal distribution). In this case, both the mean and the median would be good measures of center, but this isn't where the median is specifically the best.

3. **A bar graph with a majority of values measured above 4 y.**
- This description is vague. If there are outliers in this distribution, the median could serve well. Without further information, it's hard to determine its suitability.

4. **A bar graph that steeply rises to 30 y then steeply drops to values above 2 y.**
- This distribution also seems to have a skew (likely right skewed). In this case, the median would be favored over the mean due to the impact of higher values on the mean.

Based on the descriptions, the following options would be those where the median is the best measure of center:

- **First option** (the one that gradually rises then drops).
- **Fourth option** (that steeply rises then drops).

Thus, the first and fourth options are the correct ones where the median is the best measure of center.