# Raw Score Calculator

Instructions: Use this Raw Score Calculator to transform a z-score into a raw score. Please provide the information required below:

Z-score =
Population Mean ($$\mu$$) =
Population St. Deviation ($$\sigma$$) =

## How Do You Compute a Raw Score?

The first thing we need to understand is that a raw score is associated to a z-score. This is, for a given normal distribution, for a given mean $$\mu$$ and standard deviation $$\sigma$$, a z-score is uniquely associated with only one raw score.

This unique association between raw-scores and z-scores makes us see them as equivalent scores: This is, they are different numbers but they represent the same thing. Or rather, they contain the same information.

### Connection Between z-scores and raw scores

Now that we know about this association, we also know that a z-score is obtained from normalizing the raw score. So, how do we get a raw score from a z-score? Well, let us recall the formula of how we compute a z-score:

$Z = \displaystyle \frac{X-\mu}{\sigma}$

Then, in order to find the raw score ($$X$$), we just need to solve for it, so we get:

$X = \mu + Z \times \sigma$

### Raw Score Example

Say that you have a normal distribution with mean $$\mu = 4$$ and standard deviation $$\sigma = 2$$. Say that we have a z-score equal to $$Z = 2.5$$. What is the raw score? Using the formula above, we find that

$X = \mu + Z \times \sigma = 4 + 2.5 \times 2 = 9$

Alternatively, you may be interested in using our z-score calculator with steps, if you are provided with a raw score and need to get the z-score. Or you may be interested in computing probabilities associated to the standard normal distribution, in which case you could use our z score area calculator.

In case you have any suggestion, or if you would like to report a broken solver/calculator, please do not hesitate to contact us.