Q1: What is the main difference between range and Mean Absolute Deviation?
The range only measures the span between the single largest and single smallest values in a set, ignoring all numbers in between. Mean Absolute Deviation evaluates every single data point, providing a complete measurement of how the entire distribution behaves around its center.
Q2: Can the Mean Absolute Deviation ever be a negative number?
No. Because absolute values represent distance on a number line, every calculated deviation is positive or zero. Dividing a sum of positive numbers by a positive count will always yield a positive number or zero.
Q3: How do I know whether to compare data using Mean/MAD or Median/IQR?
Use Mean and MAD when the data distribution is relatively balanced, bell-shaped, and free of extreme outliers. When data is skewed or contains massive outliers that distort the average, rely on Median and Interquartile Range (IQR) instead.
Q4: Why does i-Ready ask for the difference between means as a multiple of the MAD?
This calculation prepares students for advanced statistics by introducing the concept behind effect size. Expressing the difference between two averages as a multiple of their variability confirms whether the gap between groups is meaningful or just random noise.
