Ever tried to tell if two sets of i-Ready scores really differ, or if you’re just looking at random noise?
Most teachers stare at average scores, nod, and move on. But the story hidden in the data often gets lost—especially when you ignore how spread out those scores are. That’s where the mean and the mean absolute deviation (MAD) step in, hand‑in‑hand, to give you a clearer picture That's the part that actually makes a difference..
What Is Using Mean and Mean Absolute Deviation to Compare Data i-Ready
When you pull a batch of i-Ready diagnostics—say, a class’s reading growth over a semester—you’ve got two numbers that can guide your next instructional move: the mean (the average score) and the mean absolute deviation (a measure of how much each student’s score strays from that average) And it works..
The mean is simple: add up every student’s score, divide by the number of students, and you’ve got a single figure that says “typical performance.”
MAD is a bit less obvious but equally useful. Take each student’s distance from the mean, ignore the sign (so you treat a score 5 points above the mean the same as one 5 points below), add those distances together, then divide by the number of students. The result tells you, on average, how far students are scattered around that central point Simple as that..
In plain English, the mean tells you where the class sits, while MAD tells you how consistent that performance is Worth keeping that in mind..
Where the Mean Shows Up in i-Ready
- Overall growth: Compare pre‑test and post‑test means to see if the class moved forward.
- Benchmark placement: Align the mean with i-Ready’s proficiency levels (Below, Approaching, On‑Track, Advanced).
Where MAD Becomes the Hero
- Identifying outliers: A high MAD flags a wide spread—maybe a few students are pulling the average up or down.
- Tailoring interventions: Low MAD means most kids are clustered; a single targeted lesson might lift the whole group.
Why It Matters / Why People Care
Imagine two classrooms both reporting a mean reading score of 78. One class has a MAD of 4; the other a MAD of 15.
If you only look at the mean, you’d assume they’re equally ready for the next grade‑level text. In practice, the low‑MAD class is tight‑knit—most kids are hovering around 78, so a single lesson on inference could push the whole group higher.
The high‑MAD class, however, is a mixed bag: some kids are at 90, others stuck at 60. A blanket lesson will help the 60‑pointers but might bore the 90‑pointers. Knowing the MAD changes your instructional strategy overnight It's one of those things that adds up..
Real talk: schools that ignore dispersion end up wasting time, money, and—worst of all—student motivation. The short version is: mean gives you the what, MAD gives you the how.
How It Works (or How to Do It)
Below is a step‑by‑step guide you can follow the next time you log into i‑Ready and pull a report.
1. Export the Data
- Open your i‑Ready dashboard.
- figure out to Reports → Diagnostic → Student Scores.
- Choose the date range (e.g., Fall 2024).
- Click Export → CSV.
You’ll get a spreadsheet with each student’s ID, pre‑test score, post‑test score, and growth Worth keeping that in mind..
2. Calculate the Mean
Open the CSV in Excel or Google Sheets.
- Formula:
=AVERAGE(range) - Example:
=AVERAGE(C2:C31)for a class of 30 students.
Write the result in a cell labeled “Mean Score.”
3. Compute the Absolute Deviations
Create a new column called |Deviation|.
- In the first row, type:
=ABS(C2 - $Mean$)(replace$Mean$with the cell containing your mean). - Drag the formula down to fill the column.
Now you have each student’s distance from the average, regardless of direction.
4. Derive the Mean Absolute Deviation
- Formula:
=AVERAGE(|Deviation| column) - Example:
=AVERAGE(D2:D31).
Label this cell “MAD.”
5. Compare Two Groups
Say you want to see if the 5th‑grade reading cohort performed differently from the 6th‑grade cohort.
- Repeat steps 1‑4 for each grade.
- You’ll end up with two means and two MADs.
Now you can answer questions like:
- Which grade has a higher average? Look at the means.
- Which grade is more consistent? Look at the MADs.
6. Visualize for Clarity
A quick bar chart for means and a side‑by‑side box plot for spread does wonders.
- In Excel: Insert → Chart → Bar for means.
- For spread: Insert → Box & Whisker (or use a scatter plot with error bars representing MAD).
Seeing the data visually often sparks the “aha!” moment for teachers and administrators alike.
Common Mistakes / What Most People Get Wrong
-
Treating the mean as the whole story
Most teachers stop after the average, assuming it captures everything. That’s the first red flag But it adds up.. -
Confusing MAD with standard deviation
They’re both dispersion measures, but MAD is less sensitive to extreme outliers. If you need a dependable picture of typical spread, MAD is often the better choice And that's really what it comes down to.. -
Skipping the absolute step
Some folks accidentally average the raw deviations, which cancels out positives and negatives and gives you zero. The whole point of MAD is to ignore direction. -
Using the wrong denominator
When you calculate MAD, always divide by the total number of observations, not by (n‑1). That’s a bias reserved for sample standard deviation, not MAD. -
Ignoring sample size
A mean of 80 with a MAD of 2 looks great, but if it’s based on two students, it’s meaningless. Always pair these stats with the class size Nothing fancy..
Practical Tips / What Actually Works
-
Pair MAD with a quick histogram. If the histogram is bell‑shaped, MAD is doing its job. If it’s jagged, consider a deeper dive (maybe split the class into sub‑groups) That's the part that actually makes a difference..
-
Set thresholds. In my district we flag any class with a MAD above 12 points for a “spread review.” It’s a simple rule that catches the outlier‑heavy groups early Still holds up..
-
Use MAD to drive grouping. When you see a high MAD, try forming flexible instruction groups (e.g., 70‑79, 80‑89, 90‑100). You’ll notice faster progress because each group works at its own level That alone is useful..
-
Communicate the story. When you present data to parents or administrators, start with the mean, then say, “But look, the spread is X, meaning most students are within Y points of that average.” It shows you’re data‑savvy, not just number‑pushing.
-
Re‑calculate after interventions. Run the same mean‑MAD analysis after a month of targeted instruction. A drop in MAD tells you the class is becoming more cohesive—often a better sign than a modest rise in the mean Not complicated — just consistent..
FAQ
Q1: Is MAD better than standard deviation for i‑Ready data?
A: For most classroom‑level reports, yes. MAD isn’t skewed by a single extreme score, so it reflects the typical student experience more honestly Not complicated — just consistent. But it adds up..
Q2: Can I use MAD for growth scores, not just raw scores?
A: Absolutely. Treat the growth numbers the same way—average the growth, then compute the absolute deviations. It tells you how uniformly students are improving Easy to understand, harder to ignore..
Q3: What if my class has a very small sample size?
A: Be cautious. With fewer than 10 students, both mean and MAD can swing wildly. Consider aggregating across multiple sections or using a rolling average over several weeks It's one of those things that adds up..
Q4: Do I need special software to calculate MAD?
A: No. Excel, Google Sheets, or even a basic calculator will do. The key is the ABS function and averaging the results.
Q5: How often should I run this analysis?
A: At least once per grading period (quarterly). If you’re running a targeted intervention, add a mid‑point check to see if the MAD is moving in the right direction.
So there you have it. In practice, the mean tells you where the class stands; the mean absolute deviation shows you how steady that standing is. Use both, and you’ll move from “we have a score of 78” to “most of our kids are clustered around 78, and here’s how we can lift the outliers.
Next time you open i‑Ready, pull those numbers, run the quick MAD routine, and watch your instructional decisions get a data‑driven boost. Happy analyzing!
