Home
Back
Z-Score to Value Formula:
| From: | To: |
The Z-Score to Value conversion transforms standardized scores back to their original measurement scale. This is useful when you need to interpret standardized values in their original context.
The calculator uses the formula:
Where:
Explanation: The formula reverses the standardization process, converting a z-score back to its original value in the distribution's units.
Details: Converting z-scores back to raw values is essential for interpreting standardized results in their original context, making decisions based on actual measurement units, and communicating results to non-technical audiences.
Tips: Enter the z-score (can be positive or negative), the standard deviation (must be positive), and the mean of the distribution. The calculator will compute the corresponding raw value.
Q1: When would I need to convert a z-score back to a raw value?
A: When you need to interpret standardized results in their original units, such as determining actual test scores from standardized values or converting normalized data back for practical application.
Q2: Can the z-score be negative?
A: Yes, negative z-scores indicate values below the mean, while positive z-scores indicate values above the mean.
Q3: What if my standard deviation is zero?
A: A standard deviation of zero means all values are identical, making z-scores undefined. The calculator requires a positive standard deviation.
Q4: How precise are the results?
A: The calculator provides results with 4 decimal places, but the actual precision depends on your input values and measurement context.
Q5: Can this be used for population parameters and sample statistics?
A: Yes, the formula works the same whether you're using population parameters (μ, σ) or sample statistics (x̄, s).