Raw Score Calculator
Provide a distribution's mean and standard deviation to convert z-scores to raw scores and vice versa.
Raw score: 625.0000
z-score: 1.5000
How to Use This Calculator
- Enter the distribution mean and standard deviation.
- Convert z to raw by providing a z-score; convert raw to z by providing a raw value.
- Use the results to interpret standardized exam scores, percentiles, or other normal metrics.
- Ensure the underlying distribution is approximately normal for meaningful comparisons.
Formula
Raw score = μ + zσ
z-score = (x − μ) / σ
Full Description
Standardized z-scores express how many standard deviations a raw score lies from the mean of a normal distribution. They enable comparisons across scales and facilitate probability calculations from the standard normal table.
Converting back to raw scores contextualizes standardized metrics in original units, such as test scores or measurement values.
Frequently Asked Questions
What if σ is zero?
A zero standard deviation implies no variability; z-score conversion is undefined. Provide σ > 0.
Can z-scores be greater than 3?
Yes, though rare in normal data. Large |z| indicates extreme observations.
Do z-scores require a normal distribution?
Z-scores are most meaningful for approximately normal distributions; otherwise, interpretations may be misleading.
How do percentiles relate?
Percentiles can be converted to z using the inverse normal CDF, then to raw scores with μ + zσ.