Z score Calculator to make your Calculation Simple

Z Score Calculator and Z-Score Table: Calculate Standard Scores and Interpretations with Allcalculator.net

Allcalculator.net, your trusted source for statistical calculations. Our Z Score Calculator is a powerful tool that allows you to quickly and effortlessly calculate the z-score for a given data point. The z-score, also known as a standard score, provides valuable insights into how far a data point deviates from the mean value. With Allcalculator.net's user-friendly interface, you can calculate z-scores within seconds, making it a convenient and efficient tool for statistical analysis. Trust Allcalculator.net to provide you with accurate and reliable z-scores for your data analysis needs.

A z-Score ranges from -3 from the left of the normal distribution curve to +3 standard deviation on the right of the normal distribution curve. To calculate the Z score using a calculator, one needs to know the mean value μ and standard deviation σ 

Z-scores allow results to be contrasted with those of a "normal" population. 

There are numerous outcomes and unit combinations for test or survey findings, and those outcomes can mean nothing at times. If you wish to compare someone's weight to the "average" person's weight, for instance, knowing that they weigh 150 pounds may be useful information, but looking at a large table of data can be meaningless (especially when weights are measured in other units). A Z-score can show you how that person's weight compares to the mean weight of the general population.

This Z score calculator used the formula for Z score as

z = (x – μ) / σ

For instance, you secured a score of 180, the mean for the test score (μ) of 140, and a standard deviation  (σ) of 40. Considering the normal distribution, calculate the Z score

z = (x – μ) / σ
(180 – 140) / 40 = 1

The Z score denotes how many standard deviations your score is from the mean. Your score is one standard deviation above the mean in this instance.

There is another formula for the Z score

The z-score formula is also visible on the left. This formula is identical to z = x – μ / σ with the exception that x (the sample mean) and s (the sample standard deviation) are used in place of (the population means) and, respectively, (the population standard deviation). However, the steps to solve it are the same even in the Z score calculator.

Use this z-score formula when you have numerous samples and want to represent the standard deviation of those sample means (the standard error):
z = (x – μ) / (σ / √n)

The number of standard errors between the sample and the population means is shown by this Z-score.

To determine the Z score normal distribution graph and the z-table can help anyone to understand what 2.0 in a Z-score denotes, which is nothing but "higher than average." The zero is present in the middle of the Z score. Positive z-scores are denoted on the right of the mean, and negative Z-scores are denoted on the left. You may determine what percentage of the population is above or below your score by looking up your score in the Z-table. 

The user had to feed the following data into the Z score calculator to calculate the average Z score.
Raw score x
Mean population μ
Standard deviation σ

The result of the Z score will be depicted based on the graphical representation with the limits and based on the score mentioned. 

Z score and probability converter

Z score and probability converter help the user to calculate and determine the likelihood of two events and a normal distribution.

Probability between Z scores
For which one has to feed
Left bound Z1  
Right Bound Z2

Z-score table

The Z-score table aids in determining the proportion of values in a typical normal distribution that falls below (to the left) a given Z-score.

Purpose of the Z score table

A Z-table provides the area under the curve to the left of a Z-score, also referred to as the standard normal table. The likelihood that Z-values will fall within a particular region of the standard normal distribution is shown by this region.