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Raw Score Calculator

Enter the Z-score, population mean, and standard deviation in the raw score calculator to determine the corresponding raw score values.

Sample Population

Population Mean(μ)

Standard Deviation(σ)

Raw Score:

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A raw score calculator helps determine the actual value of a data point using the Z score, mean, and standard deviation. The raw score represents the original measurement in a dataset before any standardization.

What Is a Raw Score?

A raw score is the original, unaltered value from a dataset. It is commonly denoted as X. While raw scores and Z scores are different numerically, they provide the same information in terms of distribution. You can convert a raw score to a Z score using a Z score calculator, or reverse the process using a raw score calculator.

Formula for Raw Score:

Raw Score = Mean + (Z Score × Standard Deviation)

X = μ + Zσ

Where:

X = Raw Score
μ = Mean
Z = Z Score
σ = Standard Deviation

How to Calculate a Raw Score?

Here are some examples to illustrate how to calculate raw scores.

Example 1:

Find the raw score of a house price with a Z score of 2.3, mean price $300,000, and standard deviation $20,000.

Solution:

X = μ + Zσ

X = 300,000 + (2.3 × 20,000)

X = 300,000 + 46,000

X = 346,000

The raw score of the house price is $346,000.

Example 2:

Calculate the raw score of an exam where the Z score is 2.5, the mean score is 60, and standard deviation is 5.

Solution:

X = μ + Zσ

X = 60 + (2.5 × 5)

X = 60 + 12.5

X = 72.5

The raw score for the exam is 72.5.

Using a Raw Score Calculator

A raw score calculator simplifies these calculations:

Input:

Enter the Z score
Provide the mean and standard deviation
Click "Calculate"

Output:

The raw score value

FAQs

How to Convert Raw Score into a Scaled Score?

Raw scores can be converted into scaled scores for easier interpretation using the formula:

Scaled Score = (Raw Score + 15) / 2

References:

From the source of tutorialspoint.com: Raw Score, Calculation and Explanation

From the source of professionals.cid.edu: Standard Scores and Raw Scores

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