Convert between raw scores and z-scores for a normal distribution.
A z-score (standard score) indicates how many standard deviations a data point is from the mean. A positive z-score means the value is above the mean; negative means below. Z-scores are used in statistics to compare values from different distributions and to find probabilities under the normal curve.
z = (x − μ) / σ. To convert a z-score back to a raw score: x = μ + z × σ.
A z-score of 0 means the raw score is exactly equal to the mean of the distribution. The value is at the 50th percentile in a standard normal distribution, right at the center.
A z-score of 2 means the raw score is 2 standard deviations above the mean. In a normal distribution, approximately 95% of values fall within z = ±2, so a z-score of 2 is relatively high (about 97.7th percentile).