Deviation Score Calculator
Compute the deviation score from the mean, standard deviation and individual score. Shows substituted working: 50 is the mean, and a 10-point difference represents one standard deviation.
Try an example
Enter the mean, standard deviation and score to see the deviation score.
Done
Deviation Score Calculator
How to use
- 1
Enter three values
Type the mean μ, standard deviation σ and individual score x.
- 2
Read the deviation score
The deviation score is computed with the formula 50 + 10 × (x − μ) ÷ σ shown step by step.
- 3
Understand the scale
A score of 50 is the mean, and each 10 points represents one standard deviation from the mean.
Features
- Deviation score from mean, standard deviation and score with substituted working
- Score 50 = mean, 10 points = one standard deviation clearly explained
- Negative scores and decimals supported; zero standard deviation reported as an error
- Inputs are never transmitted; all computation happens locally in your browser
Use cases
Analyze test results
Verify deviation scores from mock exams and regular tests.
Compare across tests
Compare performance across tests with different means and spreads.
Learn standardization
Understand the relationship between z-scores and deviation scores numerically.
Details
The deviation score standardizes a test score using the mean and standard deviation: deviation score = 50 + 10 × (x − μ) ÷ σ. A score equal to the mean gives 50; one standard deviation above gives 60; below gives 40. This allows comparison across different tests.
Each 10-point difference in the deviation score corresponds to one standard deviation (σ × 1) of difference in the raw score. With σ = 10, a 10-point score difference equals one unit. The deviation score is a relative measure based on the normal distribution and does not represent absolute ability.
Conditions: the standard deviation must be positive, and all inputs must be numeric. The deviation score reflects relative position within a group — the same raw score yields different deviation scores in different groups. Inputs are never transmitted; all computation happens locally in your browser.
FAQ
What does a deviation score of 50 mean?
It means the score is exactly equal to the group mean — half the group scored above and half below. The deviation score represents relative position within the group.
How much does the raw score change with a 10-point deviation score difference?
It corresponds to one standard deviation (σ × 1). With σ = 10, that’s a 10-point raw score difference; with σ = 15, it’s 15 points. The raw score gap varies by test.
Why does the deviation score assume a normal distribution?
Because many test score distributions are approximately normal in shape, the deviation score uses this assumption to standardize results across different tests onto the same scale.
How does the deviation score relate to z-scores?
The z-score is (x − μ) ÷ σ, the standardized value. The deviation score = 50 + 10 × z-score, scaling the z-score to a more intuitive 0–100 range centered at 50.
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Verified: Known values (μ=60,σ=10,x=80→70, μ=50,σ=15,x=100→83.33, mean→50), σ=0 errors and the English page are covered by browser tests
Did you know?
The deviation score is a relative measure: the same raw score of 80 yields a deviation score of 80 in a test with mean 50 and σ 10, but only 60 in a harder test with mean 70 and σ 10. Understanding this relativity is key to fair comparison.