1. What is the Raw Score Formula?

The raw score formula converts a standardized z-score back to the original measurement scale using the mean and standard deviation of the distribution. It's the inverse operation of standardizing a score.

2. How Does the Calculator Work?

The calculator uses the raw score formula:

Where:

• \( \mu \) — Mean of the distribution
• \( \sigma \) — Standard deviation of the distribution
• \( z \) — Standard score (z-score)

Explanation: The formula reverses the standardization process, returning a value to its original measurement scale based on the distribution parameters.

3. Importance of Raw Score Calculation

Details: Converting z-scores back to raw scores is essential for interpreting standardized results in their original context, such as test scores, measurements, or other quantitative data.

4. Using the Calculator

Tips: Enter the mean (μ) of your distribution, the standard deviation (σ), and the z-score you want to convert. The calculator will return the corresponding raw score.

5. Frequently Asked Questions (FAQ)

Q1: When would I need to convert a z-score to a raw score?
A: When you need to interpret standardized results in their original units, such as determining what test score corresponds to a particular percentile.

Q2: Can this be used for any normally distributed data?
A: Yes, as long as you know the mean and standard deviation of the distribution, this conversion is valid for any normally distributed data.

Q3: What if my data isn't normally distributed?
A: The conversion still works mathematically, but the interpretation may not be meaningful if the distribution is highly non-normal.

Q4: How precise should my inputs be?
A: Use as many decimal places as you know for accurate results, especially for the z-score which often comes from precise percentile calculations.

Q5: Can I use this for population parameters vs sample statistics?
A: Yes, just be consistent - use either population mean/SD or sample mean/SD throughout your calculations.