Question

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.

Answer 1

Mean absolute deviation (MAD) is a measure of the spread of data, with higher values indicating more spread. It is affected by outliers but to a lesser extent than other measures. A lower MAD signifies that data points are closer to the mean, reflecting less variation.

Step-by-step explanation:

The mean absolute deviation (MAD) is a measure of the variation or spread of a set of data points. It calculates the average distance between each data point and the mean of the data set. To determine the MAD, you take the absolute value of the difference between each data point and the mean, then find the average of those differences.

The statements that are true about the mean absolute deviation include:

• The mean absolute deviation is impacted by outliers, although it is less sensitive to them compared to other measures like the range or variance.
• The mean absolute deviation is a measure of variation, or spread, of the data, not a measure of center.
• The higher the mean absolute deviation is, the more spread out the data points are from the mean.

However, the statement that 'the lower the mean absolute deviation is, the more spread out the data points are from the mean' is incorrect. In fact, a lower mean absolute deviation indicates that the data points are closer to the mean, showing less variation or spread.

Answer 2

The mean absolute deviation is a measure of variation or spread in a data set. It is not affected by outliers as much as other measures of spread like the standard deviation. A higher mean absolute deviation indicates more spread in the data, while a lower value suggests data points are closer to the mean.

Step-by-step explanation:

The mean absolute deviation (MAD) is a measure used to quantify the spread or variation in a data set. Unlike the mean, median, and mode, which are measures of the center of the data, MAD measures how far, on average, all data points are from the mean of the data set. When considering the statements about MAD:

• The mean absolute deviation is impacted by outliers. - False, the MAD, similarly to the median, is less sensitive to outliers than the standard deviation because it uses absolute values rather than squared values.
• The mean absolute deviation is a measure of center of the data. - False, it is actually a measure of variability or spread of the data.
• The mean absolute deviation is a measure of variation, or spread of the data. - True, it describes how much, on average, data values deviate from the mean of the data set.
• The lower the mean absolute deviation is, the more spread out the data points are from the mean. - False, a lower MAD implies data points are closer to the mean, indicating less spread.
• The higher the mean absolute deviation is, the more spread out the data points are from the mean. - True, a higher MAD indicates that data points are more spread out from the mean, showing greater variability.