Question

determine whether each data set would be better described using the median or the mean as a measure of center. drag the tiles to the best measure of center for the data

Explanation:

Step1: Recall the properties of mean and median

The mean is sensitive to outliers. The median is less affected by outliers.

Step2: Analyze the first histogram

The first histogram has a long - tail (skewed distribution). In a skewed distribution, the median is a better measure of central tendency as the mean can be pulled by the extreme values in the tail.

Step3: Analyze the second histogram

The second histogram is also skewed. So, the median is a better measure.

Step4: Analyze the first dot - plot

The first dot - plot has outliers (values that are far from the main cluster). The median is less affected by these outliers.

Step5: Analyze the second dot - plot

The second dot - plot is more symmetric (assuming no extreme outliers that would disproportionately affect the mean). In a relatively symmetric distribution, the mean is a good measure of central tendency as the values are evenly distributed around the center and the mean can accurately represent the typical value.

Answer:

For the first histogram: Median. For the second histogram: Median. For the first dot - plot: Median. For the second dot - plot: Mean.