T Score Calculator
Convert a raw score to a T score (mean 50, SD 10) given the group mean and standard deviation.
Inputs
T Score
55.00
Z Score
0.5000
Step by step
Values used
Raw Score (x) = 75; Group Mean (μ) = 70; Group Standard Deviation (σ) = 10
Z Score
z = (x − μ) / σ
T Score
T = 50 + 10z
T Score
= 55.00
Z Score
= 0.5000
How it works
A T score rescales any normally-distributed raw score to a scale with mean 50 and standard deviation 10. It is computed by first finding the z-score, then applying T = 50 + 10z.
Formulas
Z Score
z = (x − μ) / σ
- x
- Raw score
- μ
- Mean
- σ
- Standard deviation
T Score
T = 50 + 10z
- z
- Z score
Frequently Asked Questions
What is the difference between Z score and T score?
A Z score has mean 0 and SD 1. A T score has mean 50 and SD 10. T scores avoid negative values, making them easier to interpret in educational and psychological testing.
What T score is considered average?
T scores between 40 and 60 are typically within one standard deviation of the mean and considered 'average'.