How is the Z-Score Calculated?
If you’re a student, parent, or just someone curious about how university entrance works, you’ve probably heard the term "Z-score" thrown around a lot. But what exactly is it, and how is it calculated?
Let’s break it down in plain English.
🧠 What Is the Z-Score?
In simple terms, a Z-score is a statistical value that tells you how far your exam marks are from the average score of all students in your subject stream and district.
It doesn’t just look at how much you scored – it looks at how well you did compared to others. So, two students getting the same raw marks might end up with different Z-scores if they sat the exam in different subject streams or scored differently in individual subjects.
🎓 Why Is It Important?
The Z-score plays a huge role in deciding who gets into university in Sri Lanka. Since raw marks can’t be compared fairly across subjects (for example, Physics might be harder than Biology), the Z-score is used to level the playing field.
🧮 How Is It Calculated?
Here’s the basic formula:
Z = (X - μ) / σ
Where:
- X is your total raw mark (combined score from the subjects you took),
- μ (mu) is the mean (average) of all students’ marks in your stream,
- σ (sigma) is the standard deviation, which shows how spread out the scores are.
🗂️ Step-by-Step Breakdown:
- All raw marks are collected from students in the same subject stream across the island.
- The mean (average) mark and the standard deviation are calculated.
- Your raw mark is plugged into the formula to see how far above or below the average you are.
- The resulting Z-score is used for ranking students within their stream.
📌 A Real-World Example
Let’s say you’re a student in the Commerce stream in the Colombo district, and you did:
- Accounting – 87 marks
- Business Studies – 71 marks
- Logic – 63 marks
To calculate your final Z-score, here’s how it works step by step:
1. Get the average and standard deviation for each subject in your district
Assume the following averages and standard deviations for this example (note: these are just hypothetical values for explanation):
| Subject | Mean (μ) | Std Dev (σ) |
|---|---|---|
| Accounting | 70 | 10 |
| Business Studies | 60 | 8 |
| Logic | 55 | 6 |
2. Calculate individual Z-scores
Now use the Z-score formula for each subject:
Z = (X - μ) / σ
- Accounting: (87 - 70) / 10 = 1.7
- Business Studies: (71 - 60) / 8 = 1.375
- Logic: (63 - 55) / 6 = 1.33
3. Average the Z-scores
Now, to get your final Z-score: Final Z = (1.7 + 1.375 + 1.33) / 3 = 1.468 So your final Z-score is approximately 1.47. A Z-score of 1.47 means your average performance is about 1.47 standard deviations above the mean, which is quite strong! You’ve outperformed many other students in your subject stream.
🤔 Why Doesn’t Everyone Just Get High Z-Scores?
Because Z-scores depend on relative performance. If everyone in your stream scores highly, it’s still possible to get a low Z-score if your marks are just average compared to theirs.
It also explains why sometimes people in less competitive subject streams get higher Z-scores for the same raw marks — they performed better compared to their peers.
🧩 Key Points to Remember
- Z-score isn’t your mark, it’s your position compared to others.
- It varies by stream & subjects you have selected.
- It’s essential for university admission under the free education system.
- It balances fairness between different subjects and student groups.
📝 Final Thoughts
Understanding how Z-scores work helps students and parents make sense of A/L results and university cutoffs. It’s a powerful statistical tool designed to bring equity to the system – even if it feels a little confusing at first!
So next time you hear about Z-scores, just remember: it’s not just about how much you scored – it’s about how you performed in your crowd.