Convert a raw score to a T score (mean 50, SD 10) given the group mean and standard deviation.
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.
Z Score
z = (x − μ) / σ
T Score
T = 50 + 10z
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.
T scores between 40 and 60 are typically within one standard deviation of the mean and considered 'average'.