Z Score Calculator

Introduction of Z score calculator

The z-score is a statistical measure that tells you how far a data point is from the mean, in terms of standard deviations. Imagine we have the test scores of a class. The mean (average or µ) score is 70, and the standard deviation (or σ) is 10. Let’s say a student scored (or random variable or X₀) 85. To calculate the z-score for this student’s score, we use the formula:

Plugging in the numbers:

This means the student’s score is 1.5 standard deviations above the mean. A positive z-score indicates the value is above the mean, while a negative z-score indicates it’s below the mean.

In relation to calculating probabilities for P(z > Z-score) and P(z < Z-score), these terms allow you to determine probabilities based on the standard normal distribution. For graphical representation:

• P(z < Z-score): Represents the area under the standard normal distribution curve up to the Z-score value.
• P(z > Z-score): Represents the area under the curve to the right of the Z-score value.

In the following we learn how to use the online calculator for z score.

Using an Online Z-Score Calculator

1. Enter the Values
   Fill in the input fields with the following:
   • Data Point (X): The specific value you want to evaluate.
   • Mean (μ): The average of your dataset.
   • Standard Deviation (σ): The measure of the spread of your dataset.
2. Click the Calculate Button
   Press the “Calculate” button to compute the z-score.
3. View the Result of z score
   The calculator will display the z-score:
4. View the result of P(z < Z-score) and P(z > Z-score)

Example

For instance, if:

• Data Point (X) = 85
• Mean (μ) = 70
• Standard Deviation (σ) = 10

When you enter these values and click “Calculate,” the result will show:
“Z-Score: 1.5”

The second part of this solver enables the calculation of probabilities for the two terms P(z > Z-score) and P(z < Z-score). In this example, their schematic representation can be illustrated as follows:

What is displayed in the output of this online solver is as follows:

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