A/L Z-Score Explained — Standardization Calculator
Understand z-scores and calculate one standardized value using your own population mean and standard deviation. Educational only; not an official A/L result.
Understand standardization with your own value, population mean and standard deviation. This is a learning calculator, not an official Sri Lankan A/L Z-score calculator.
Use the same units and the same population for all three inputs. Supply known statistics; do not guess an exam distribution.
Enter three known values to calculate.
What the number means
z = (x − μ) / σ measures distance from the mean in standard-deviation units. A positive z is above the mean; a negative z is below it. It has no measurement unit. Zero indicates the mean, not a zero mark.
Illustration only: x = 75, μ = 60 and σ = 10 gives z = 1.5. Changing x to 45 gives −1.5; x = 60 gives 0. These are invented teaching values, not A/L examination statistics.
Common questions
Can I calculate my official A/L Z-score from three marks?
No. This page standardizes one value using statistics you supply. It does not recreate the official examination standardization or combine subject scores. Use your official examination result for your actual Z-score.
Is z a percentage, grade or percentile?
No. A z-score is a standardized distance. A percentile needs a distribution model or empirical distribution. This tool makes no normal-distribution assumption and does not convert z to a percentile.
Where do the mean and standard deviation come from?
Use verified statistics for the population relevant to the value. The mean and standard deviation must describe that same population in the same units. If they are unknown, this calculation cannot establish your position.
Check the stated data sources and assumptions before relying on a result.