Final answer:
The mean absolute deviation is affected by outliers, is a measure of spread, and a higher value indicates more spread out data. It is not a measure of the center of the data, which is represented by the mean, median, and mode. The lower the mean absolute deviation, the closer the data points are to the mean.
Step-by-step explanation:
True statements about the mean absolute deviation would include that it is impacted by outliers and that it 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. In contrast, the lower the mean absolute deviation indicates that the data points are closer to the mean, not more spread out. Mean Absolute Deviation (MAD) helps quantify the spread of a data set by calculating the average distance each data point is from the mean of the data set.
It is important to note that the mean absolute deviation is not a measure of the center of the data; instead, measures like the average (arithmetic mean), median, and mode serve this purpose. The center of the data set provides a central point that the data clusters around, while measures like MAD and standard deviation describe how spread out the data is from this center point.
The presence of outliers can affect the mean absolute deviation because they can increase the average distance that the data points fall from the mean. However, the mean absolute deviation is less sensitive to outliers than the standard deviation is because it does not square the deviations; it takes the absolute value of differences.