Z Score to Raw Score Calculator




Z Score Formula




Z score
Mean, µ
Standard deviation, σ
Raw Score:


This Z score to raw score calculator calculates the raw score value based on the z score, mean, and standard deviation.

The raw score computed is the actual score, or value, obtained.

If you want to calculate the z score based on the raw score, mean, and standard deviation, see Z Score Calculator.

The z score is the numerical value which represents how many standard deviations a score is above the mean.

The z score, thus, tells us how far above or below average a score is from the mean by telling us how many standard deviations it lies above or below the mean.

Using the z score, as well as the mean and the standard deviation, we can compute the raw score value by the formula, x= µ + Zσ, where µ equals the mean, Z equals the z score, and σ equals the standard deviation.

So, for example, if we have a z score of 1.5, a mean of 80, and a standard deviation of 10, this means that the raw score that was obtained is, raw score= µ + Zσ = (80) + (1.5)(10)= 95.

To make this example even clearer, let's take a set of numbers to illustrate the raw score values. Let's say for the SAT, the average MATH score is 500 and the standard deviation for the test for all students who took it is 100. Being that the mean is again 500, if most people score within 1 standard deviation of the mean, this is the equivalent of z scores of -1 and 1 for the lower and upper standard deviations. This means that if z scores of -1 and 1 are converted into their raw score values, most students scored between a 400 and 600 on the exam. A z score of -2 and 2 means that students scored between 300 and 700.

To use this calculator, a user just enters the z score, the mean (or average) of the scores, and the standard deviation, and then clicks the 'Calculate' button. The result will automatically be calculated and shown.

Calculating the raw score can be used for all types of data sets. Raw scores give the actual score, while z scores are used to show how much variance a piece of data is from its mean. Both are gauges that quantify where we stand for a particular situation.

Example Calculations

Find the raw score for a housing price when the house's z score is 2.5, the average mean for houses in the area is $280,000, and the standard deviation is $12,000.

Answer:

x= µ + Zσ

z-score= $280,000 + (2.5)($12,000)= $300,000

So the raw score is $300,000.

Find the raw score for an exam when the z score is 1.8, the average mean for the test is 70, and the standard deviation is 15.

Answer:

x= µ + Zσ

x= 70 + (1.8)(15)= 97

So the raw score is 97.

Related Resources

Expected Value Calculator

Area Under the Curve Calculator

Confidence Interval Calculator