Raw Score Calculator
Convert between raw scores and standardized scores using Z-score, mean, and standard deviation
Calculate Raw Score Parameters
Choose which parameter you want to find
Standardized score
Population or sample mean
Population or sample standard deviation
Calculation Results
Formula Used
Interpretation
The raw score of 48.000 is below the mean, indicating below-average performance.
Step-by-Step Example
Example Problem
Scenario: A student takes a math quiz
Z-score: -4 (4 standard deviations below mean)
Standard deviation: 3 points
Mean: 60 points
Find: The student's raw score (actual points)
Solution Steps
1. Use the raw score formula: X = Z × σ + μ
2. Substitute values: X = (-4) × 3 + 60
3. Calculate: X = -12 + 60
4. Result: X = 48 points
Interpretation: The student scored 48 points, which is 4 standard deviations below the average.
Key Formulas
Z-score Interpretation
Quick Tips
Raw scores are unaltered, original measurements
Z-scores standardize data for comparison
Positive Z-score = above average
Negative Z-score = below average
Standard deviation must be positive
Understanding Raw Scores
What is a Raw Score?
A raw score is an unaltered, original data point or measurement. It represents the actual numerical value obtained from a test, assessment, or observation before any statistical transformation or standardization.
Why Use Raw Scores?
- •Foundational data for statistical analysis
- •Convert to standardized scores for comparison
- •Calculate percentiles and grade equivalents
- •Determine relative performance within a group
Key Relationships
Raw scores are connected to standardized scores through the mean and standard deviation of the distribution. This relationship allows us to understand how an individual score compares to the group average.
Applications
- •Educational testing and assessment
- •Psychological and cognitive evaluation
- •Quality control in manufacturing
- •Research and data analysis