You take your x-value, subtract the mean , and then divide this difference by the standard deviation. This gives you the corresponding standard score (z-value or z-score). Standardizing is just like changing units (for example, from Fahrenheit to Celsius).

Every score stays in the exact same position relative to every other score in the distribution. Mean – when raw scores are transformed into z-scores, the mean will always = 0.

Raw scores are the observed values of the variables. Deviation scores are obtained by subtracting the mean from the raw scores, deviation score = x = (X – mean). Deviation scores have a mean = 0 and the same standard deviation as the raw scores.

z = (x – μ) / σ For example, let’s say you have a test score of 190. The test has a mean (μ) of 150 and a standard deviation (σ) of 25. Assuming a normal distribution, your z score would be: z = (x – μ) / σ

A Z-score is a numerical measurement that describes a value’s relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. A Z-Score is a statistical measurement of a score’s relationship to the mean in a group of scores.

Solution: The raw score formula is simply the z-score formula solved for x, the raw score. Depending on what your distribution represents, start by either writing the formula for the raw score of a population: x = μ + zσ.

The equation for z-score of a data point is calculated by subtracting the population mean from the data point (referred to as x) and then the result is divided by the population standard deviation. Mathematically, it is represented as, Z Score Formula = (x – μ) / ơ.

Z = (x – mean)/standard deviation. Assuming that the underlying distribution is normal, we can construct a formula to calculate z-score from given percentile T%. #P(X P( Z < (x_0-//mu)/ sigma ) = T #. #=> (x_0 -//mu)/sigma = # InvNorm(T)

Standard Normal Table finds the probability from 0 to Z, while Excel calculates from infinity to Z. Therefore, if you are trying to get the same result as Standard Normal Table does, subtract 0.5 by the Excel result and then apply absolute value. For example, for Z score = 2.41, probability = 0.492 according to the Standard Normal Table.