Z Score Calculator

How to Use the Z-Score Calculator

Welcome to the Z-Score Calculator! This detailed guide will help you understand how to use the calculator to compute the Z-Score, determine the percentile, and interpret the result as standard deviations from the mean. Please follow the steps outlined below:

Step 1: Enter Observed Value

Begin by entering the observed value, also known as the value you want to standardize. Locate the input field labeled Observed Value (x) and input your data point. This value is mandatory for the calculation process.

Step 2: Input the Population Mean

Next, input the population mean. Find the field labeled Population Mean (μ). This is the average value of the dataset you are analyzing. Enter the mean value accurately, as it will impact your Z-Score calculation.

Step 3: Provide the Standard Deviation

In the third step, you need to enter the standard deviation of your dataset. Use the field labeled Standard Deviation (σ). Note that the standard deviation must be a positive number, greater than or equal to 0.000001, and is essential for calculating a meaningful Z-Score.

Step 4: Calculate and Analyze the Results

After entering all the required inputs, the calculator will compute the results based on the provided data.

• Z-Score: The calculator will output the Z-Score in the field labeled Z-Score. The Z-Score is calculated using the formula: (observedValue – populationMean) / standardDeviation.
• Percentile: Utilize the Z-Score to determine where the observed value stands in comparison to the rest of the dataset. The field labeled Percentile displays the result using the formula: (0.5 * (1 + erf(zScore/sqrt(2)))) * 100. The result is shown as a percentage.
• Interpretation: Check the field labeled Standard Deviations from Mean to understand how many standard deviations away from the mean your observed value is. The absolute value of the Z-Score provides this interpretation.

That’s it! By following these steps, you can effectively use the Z-Score Calculator to standardize values and analyze your dataset. Ensure all entries are correct for an accurate calculation.