Z Calculator

How to Use the Z-Score Calculator

Introduction

This guide explains the step-by-step process to use the Z-Score Calculator for calculating the Z-Score, Percentile, and Probability (Area under the curve) of a given raw score. Follow the instructions below to input your data and understand the results provided by the calculator.

Step 1: Prepare Your Inputs

Before using the calculator, ensure you have the necessary data ready. You will need the following:

• Raw Score (X): This is the observed value that you are evaluating.
• Population Mean (μ): The mean value of the population data.
• Standard Deviation (σ): The standard deviation of the population data.

Step 2: Input Your Data

Follow these sub-steps to input your data into the calculator:

• Locate the field for Raw Score (X) and enter the observed value. This field is required and supports two decimal places.
• Locate the field for Population Mean (μ) and input the mean of your population data. This value is also required and supports two decimal places.
• Locate the field for Standard Deviation (σ), enter the standard deviation of your data. This input must be a positive number with no less than 1e-06 and supports two decimal places.

Step 3: View the Results

After entering your data, the calculator will automatically perform the necessary calculations and display the following results:

• Z-Score: The Z-Score is calculated using the formula: (rawScore – mean) / stdDev. It provides the number of standard deviations the raw score is from the mean. The result is displayed with four decimal places.
• Percentile: Using the Z-Score, the calculator computes the percentile rank with the formula: (0.5 * (1 + erf(zScore/sqrt(2)))) * 100. This represents the percentage of scores in a normal distribution that fall below the raw score and is shown with two decimal places followed by a percentage sign.
• Probability (Area under the curve): This value indicates the probability of the raw score and is computed with the formula: 0.5 * (1 + erf(zScore/sqrt(2))). The output is presented in percentage format with four decimal places.

Conclusion

This guide sums up using the Z-Score Calculator to analyze your data. By inputting the raw score, population mean, and standard deviation, you can quickly obtain the Z-Score, percentile, and probability, aiding in statistical analysis and decision-making.