Raw Score Calculator

In statistics, a Z-score represents how many standard deviations a specific data point lies above or below the population mean. To reverse this transformation and find the original raw score, the calculator uses the standard linear equation: X = mu + (sigma * z), where X represents the raw score, mu is the mean value of the population, sigma is the standard deviation, and z is the Z-value. By multiplying the Z-score by the standard deviation and adding the result to the mean, you recover the exact position of the data point in its original unit of measurement.

Imagine you are analyzing a college entrance exam where the historical mean score (mu) is 100, and the standard deviation (sigma) is 15. A particular applicant achieves a Z-score (z) of 1.20, indicating strong performance above average. To find their exact raw score, substitute the values into the formula: Raw Score = 100 + (15 * 1.20). First, multiply 15 by 1.20 to get 18. Then, add 18 to the mean of 100, resulting in a raw score of 118. This means the applicant scored 118 points on the exam.

Always verify the sign of your Z-score; a negative Z-score indicates a value below the mean and must be subtracted rather than added in intuitive checks. Ensure that your mean and standard deviation come from the same reference population to maintain statistical validity. When handling decimal values, keep consistent precision across all inputs to prevent rounding errors from skewing your final outcome.