Question

describing mean absolute deviation
which statements are true about mean absolute deviation? select all that apply.
□ the mean absolute deviation is impacted by outliers.
□ the mean absolute deviation is a measure of center of the data.
□ the mean absolute deviation is a measure of variation, or spread, of the data.
□ the lower the mean absolute deviation is, the more spread out the data points are from the mean.
□ the higher the mean absolute deviation is, the more spread out the data points are from the mean.

Explanation:

1. Statement 1: Outliers are extreme values. Since mean absolute deviation (MAD) involves distances from the mean, outliers (which are far from the mean) will increase the distances, so MAD is impacted by outliers. This is true.
2. Statement 2: Measures of center (like mean, median, mode) describe the middle of the data. MAD describes how spread out data is (variation), not center. So this is false.
3. Statement 3: MAD calculates the average distance of data points from the mean, which measures how spread out (variation) the data is. So this is true.
4. Statement 4: A lower MAD means data points are closer to the mean (less spread out), not more. So this is false.
5. Statement 5: A higher MAD means data points are farther from the mean (more spread out). So this is true.

Answer:

• The mean absolute deviation is impacted by outliers.
• The mean absolute deviation is a measure of variation, or spread, of the data.
• The higher the mean absolute deviation is, the more spread out the data points are from the mean.