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Raw Score Calculator

Created by Anna Oppenheim
Reviewed by Steven Wooding
Last updated: Jun 06, 2023


The raw score calculator helps you to find the original, unaltered data point or value!

In statistics, the raw score is simply a score that has not been transformed or standardized. It's frequently used to represent a person's actual score or measurement on a test or assessment. Read on to learn more about:

  • What is a raw score?
  • What is a raw score formula?
  • How to find a raw score!

What is a raw score?

A raw score (or an observed score) is a single piece of unaltered data. It is the simplest measurement form, representing the actual numerical value or quantity assigned to a particular response or performance on a test, questionnaire, or assessment task. For example, if a student answers 25 out of 30 questions correctly on a math test, their raw score is 25. But the total number of questions does not change the raw score. If a student answers 25 out of 100 questions correctly, the raw score is still 25. If another student gets 30 points thought, the raw score of this student would be 30.

Raw scores serve as a foundational component in various statistical analyses. However, they can be helpful for initial comparisons or ranking of individuals, but they may not provide a complete understanding of performance.

Taking the example from above, if a student's raw score is 25 out of 30 is a good result, but 25 out of 100 might not be. Therefore raw scores are often used to calculate other types of scores, such as percentage scores, grade point averages, or standardized scores like z-scores. Later these calculations help standardize measurements and provide additional information about an individual's performance compared to a larger group or population, for example, students among the rest of the class.

Raw scores can be expressed in different units, depending on the test's or assessment's nature. For example, a raw score on a multiple-choice test might be the number of questions answered correctly, while a raw score on an essay test might be the number of points awarded by the grader.

How to find a raw score?

You need to know the distribution parameters to calculate the raw score (X). That means that you need the z-score (Z), the mean (μ), and the standard deviation (σ).

The raw score formula is:

X=Z×σ+μX = Z \times σ + μ

🔎 To know what are and how to calculate other parameters check our:

Raw score calculation example

Let's say we're trying to determine the test results, meaning raw score (X), for a math quiz for one particular student. Going step by step:

  • We know that this certain student has a quiz score with a z-score (Z) of -4.
  • We also know the standard deviation (σ) of the quiz of 3.
  • Last but not least, the mean (μ) of the exam was 60 points.

Now we simply need to apply the raw score formula:

  1. X = -4 × 3 + 60
  2. X = -12 + 60
  3. X = 48

This student got 48 points on the math quiz!

How to use the raw score calculator

First, as in the example above, you need three parameters:

  • The z-score (Z);
  • The standard deviation (σ); and
  • The mean (μ)

The next step is to put those parameters in the calculator. Once you will do that, the calculator will compute the raw score!

⚠️ Remember to ensure that all the parameters (z-score, mean, and standard deviation) are based on the same data set!

Our calculators also work backward! If you have the raw score and you have two other parameters (for example, the mean (μ) and the x-score (Z)), you can determine the standard deviation (σ)!

❗ If the raw score is less than the mean, Z-score must be negative! And the other way around, if the raw score is greater than the mean, Z-score has to be positive.

Anna Oppenheim
Mean value (μ)
Standard deviation (σ)
Z-score (z)
Raw score (X)
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