Question

1. the mean absolute deviation of a data set is 4.5. what does this tell you about the data?

a. the average value in the data set is 4.5
b. on average, the data points are 4.5 units away from the mean
c. the range of the data is 4.5
d. the median of the data is 4.5

Explanation:

To solve this, we recall the definition of mean absolute deviation (MAD). The MAD measures the average distance between each data point and the mean.

• Option A: The average value of the data set is not what MAD represents. MAD is about deviation from the mean, not the average value of the set.
• Option B: The mean absolute deviation is calculated as the average of the absolute differences between each data point and the mean. So, it tells us that, on average, the data points are a certain distance (here 4.5) away from the mean. This matches the definition of MAD.
• Option C: Range is the difference between maximum and minimum values, unrelated to MAD.
• Option D: Median is the middle value, not related to MAD.

Answer:

B. On average, the data points are 4.5 units away from the mean