Enter the Z score and standard deviation into the calculator to determine the raw score. This calculator can also evaluate any of the variables given the others are known.

Inverse Z Score Formula

The following formula is used to calculate the inverse Z score.

X = μ + Zσ


  • X is the raw score μ is the mean of the population Z is the Z score σ is the standard deviation of the population

To calculate the raw score, multiply the Z score by the standard deviation of the population. Then, add the mean of the population to the result. This will give you the raw score, which is the original value before it was standardized.

What is a Inverse Z Score?

An inverse Z score, also known as a Z-score to raw score conversion, is a statistical method used to determine the original raw score of a data point given its Z-score and the mean and standard deviation of the dataset. The Z-score represents how many standard deviations a data point is from the mean. The inverse Z-score is calculated by multiplying the Z-score by the standard deviation and adding the mean. This is useful in understanding the original value of a data point in the context of its dataset.

How to Calculate Inverse Z Score?

The following steps outline how to calculate the Inverse Z Score.

  1. First, determine the mean of the population (μ).
  2. Next, determine the Z score (Z).
  3. Next, determine the standard deviation of the population (σ).
  4. Use the formula X = μ + Zσ to calculate the raw score (X).
  5. After inserting the values of μ, Z, and σ into the formula, calculate the Inverse Z Score (X).

Example Problem:

Use the following variables as an example problem to test your knowledge.

mean of the population (μ) = 50

Z score (Z) = 1.5

standard deviation of the population (σ) = 10