Standard Score Calculator Formula
Understand the math behind the standard score calculator. Each variable explained with a worked example.
Formulas Used
T-Score (Standard Score)
t_score = 50 + 10 * zZ-Score
z_score = zDeviation from Mean
deviation = score - meanVariables
| Variable | Description | Default |
|---|---|---|
score | Your Score | 82 |
mean | Group Mean | 75 |
std_dev | Standard Deviation | 8 |
z | Derived value= (score - mean) / std_dev | calculated |
How It Works
How to Calculate a Standard Score (T-Score)
A T-score rescales your z-score to a distribution with mean 50 and standard deviation 10.
Formula
T-Score = 50 + 10 x Z
Where Z = (Score - Mean) / Standard Deviation
T-scores eliminate negative numbers and decimals, making interpretation easier.
Worked Example
A student scores 82 in a group with mean 75 and standard deviation 8.
- 01Z-score = (82 - 75) / 8 = 0.875
- 02T-score = 50 + 10 x 0.875 = 58.75
- 03The student is above average with a T-score of 58.75.
Frequently Asked Questions
What is a T-score?
A T-score is a standard score with mean 50 and standard deviation 10. A T-score of 60 means you are one standard deviation above the mean.
When are T-scores used?
T-scores are commonly used in psychological testing, educational assessments, and clinical evaluations to compare individuals to a reference group.
What is the range of T-scores?
Most T-scores fall between 20 and 80 (within 3 standard deviations). A T-score of 50 is exactly average.
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