Z-Score Calculator

Find Z-scores and standardize datasets easily using our precise tool.

Z-Score Calculator

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Result
Z-score	1
Probability of x<5	0.84134
Probability of x>5	0.15866
Probability of 3<x<5	0.34134

Result
Z-score	2
P(x<Z)	0.97725
P(x>Z)	0.02275
P(0<x<Z)	0.47725
P(-Z<x<Z)	0.9545
P(x<-Z or x>Z)	0.0455

Result
P(-1<x<0)	0.34134
P(x<-1 or x>0)	0.65866
P(x<-1)	0.15866
P(x>0)	0.5

What is an Online Z-Score Calculator?

An Online Z-Score Calculator is a tool that computes the z-score, which measures how many standard deviations a data point is from the mean of a dataset. The z-score is calculated using the formula:

z = \frac{X - \mu}{\sigma}

Where:

$X$ = the data point,
$\mu$ = the mean of the dataset,
$\sigma$ = the standard deviation of the dataset.

The z-score helps standardize data and is used in statistics for comparing data points, determining probabilities in a normal distribution, and identifying outliers.

How to Use an Online Z-Score Calculator?

Access the Tool: Open an online z-score calculator in your browser.
Input the Values:
- Enter the data point ( $X$ ).
- Input the mean ( $\mu$ ) of the dataset.
- Enter the standard deviation ( $\sigma$ ).
Click “Calculate” or “Compute”: The tool will process the input and provide the z-score.
Interpret the Result: A positive z-score indicates the data point is above the mean, while a negative z-score indicates it is below the mean.

Frequently Asked Questions-

What does a z-score represent?
A z-score indicates how far and in what direction a data point deviates from the mean, measured in standard deviations. For example:
- $z = 1.0$ : The data point is 1 standard deviation above the mean.
- $z = -2.0$ : The data point is 2 standard deviations below the mean.
What is a “normal” z-score range?
In a normal distribution, approximately:
- 68% of data points fall within $z = -1$ to $z = 1$ .
- 95% of data points fall within $z = -2$ to $z = 2$ .
- 99.7% of data points fall within $z = -3$ to $z = 3$ .
Can I use this calculator for any distribution?
Z-scores are most meaningful in a normal distribution but can be used for any dataset as a standardized measure.
What happens if the standard deviation ( $\sigma$ ) is zero?
If the standard deviation is zero, the z-score cannot be calculated because dividing by zero is undefined.
How are z-scores used in real-world applications?
Z-scores are used in:
- Comparing scores from different datasets (e.g., test scores).
- Identifying outliers in data analysis.
- Determining probabilities in a normal distribution (e.g., finding the percentage of data points below or above a specific value).