Step-by-Step Visual Walkthrough: How to Calculate Mean and Mad on I-Ready Fast
By Marcus Vance
Consider an authentic problem modeled after adaptive diagnostic questions: Two track-and-field athletes, Marcus and Jordan, run five 100-meter sprints. Their times in seconds are logged below:
- 12.0, 12.4, 12.6, 12.8, 13.2
- 11.2, 11.8, 12.6, 13.4, 14.0
Both runners yield an identical average run time:
$$\text{Mean} = \frac{63.0}{5} = 12.6\text{ seconds}$$
To determine who delivers the more dependable performance, we calculate the step-by-step MAD calculation for each runner.
| Metric & Stage | Marcus (Dataset A) | Jordan (Dataset B) |
|---|---|---|
| Sample Size ($n$) | 5 runs | 5 runs |
| Calculated Mean ($\bar{x}$) | 12.6 seconds | 12.6 seconds |
| Distances from Mean | 0.6, 0.2, 0.0, 0.2, 0.6 | 1.4, 0.8, 0.0, 0.8, 1.4 |
| Sum of Distances | 1.6 seconds | 4.4 seconds |
| Mean Absolute Deviation | 0.32 seconds | 0.88 seconds |
| Practical Distribution Takeaway | High consistency, narrow cluster | High variability, wide dispersal |
Marcus holds a MAD of 0.32, whereas Jordan holds a MAD of 0.88. On an i-Ready assessment, the correct analytical deduction is clear: although both competitors post the same average speed, Marcus represents the more predictable sprinter because his individual attempts hover closer to his baseline average.
Marcus Vance is a cybersecurity auditor and technology writer dedicated to educating the public about online safety, data privacy regulations, enterprise security, and emerging cyber threats.
