Z Score Calculator
Z-score and Probability Converter
Probability between Two Z-scores
How to Use the Calculator
Find a z-score by entering the data value, population mean, and standard deviation into the calculator.
This helps you convert the raw value into a z-score, showing how many standard deviations the data point is from the mean.
Positive z-scores indicate values above the mean, while negative z-scores show values below the mean.
Using a z-score table, you can determine the percentage of values in the distribution that are above or below the calculated z-score. This method also enables comparison between different datasets by standardizing the scores. Always ensure the data follows a normal distribution for accurate results.
Using the Z-Score Calculator
To calculate a z-score, you need some key details. These include a raw data point, population mean, and population standard deviation.
Input these values into the calculator, and it will show the z-score.
Another method involves using a sample mean, the sample size, population mean, and population standard deviation. You input the sample mean and size along with the population values to see the result.
Alternatively, you can work with a set of sample data.
Enter these values separated by commas or spaces. The calculator processes each point or sample line automatically, accommodating entries from spreadsheets or text files. Different formats are supported for an efficient calculation experience.
Z-Score Equation
To find the z-score for a specific data point, use this equation:
[ z = \frac{x – \mu}{\sigma} ]
- z represents the standard score.
- x is the data point you’re evaluating.
- μ is the mean of the population.
- σ stands for the standard deviation of the population.
If you’re dealing with a sample and you know the population standard deviation, the equation changes slightly:
[ z = \frac{\overline{x} – \mu}{\frac{\sigma}{\sqrt{n}}} ]
- z remains as the standard score.
- (\overline{x}) represents the sample mean.
- n is the number of observations in your sample.
Acceptable Data Formatting
When listing data points, you can use different formats, such as:
Line Breaks:
42
54
65
47
59
40
53
Commas:
42, 54, 65, 47, 59, 40, 53
Spaces:
42 54 65 47 59 40 53
Mixed Separators:
42, 54 65,,, 47,, 59, 40 53
Choose the format that works best for your analysis. Keep in mind that the formula relies on precision, requiring accurate values for the mean and standard deviation.