# Z Score Calculator

Z Score calculator calculates the standard score for any raw score. Z Score is a measure that is used to describe the relationship between a raw score and the mean value of the given data set. Z scores are also called standard scores.

## What is Z Score Calculator?

Z Score Calculator is an online tool used to calculate the z score for the given mean, raw score, and standard deviation. The z score tells us the number of standard deviations by which the raw score is above or below the mean of the data. To use this ** z score calculator**, enter values in the input boxes.

### Z Score Calculator

*Use 5 digits only

## How to Use Z Score Calculator?

Use the steps given below to find the z score using the online z score calculator:

**Step 1:**Go to Cuemath’s online z score calculator.**Step 2:**Enter the values of the raw score, the mean, and the standard deviation in the input boxes of the z score calculator.**Step 3:**Click on the**"Calculate"**button to find the z score.**Step 4:**Click on the**"Reset"**button to clear the fields and enter new values.

## How Does Z Score Calculator Work?

Z score can be both positive and negative. A positive z score indicates that the raw score is above the mean. Similarly, a negative z score denotes that the raw score is below the mean. Furthermore, if we have a z score that is equal to 1, it implies that the raw score is 1 standard deviation above the mean. If the z score is -2, it shows that the raw score is 2 standard deviations below the mean of the given data. The steps to calculate the z score are as follows:

- Subtract the mean of the population from the given raw score. The mean is given by \(\mu\) while x denotes the raw score.
- Divide the value obtained in step 1 by the standard deviation to get the z score. The standard deviation is represented by \(\sigma\).

The formula for calculating the z score is given as follows:

Z score = \(\frac{x - \mu }{\sigma }\).

The calculator replaces \(\mu\) with u and \(\sigma\) by v.

## Solved Examples on Z-Score

**Example 1:** Find the Z-score for a raw score of 5, mean 3, and standard deviation 1 and verify it using the z score calculator.

**Solution:**

Given raw score x = 5, mean \(\mu\) = 3 and standard deviation \(\sigma\) = 1

z = \(\frac{x - \mu }{\sigma }\) = (5 - 3)/1 = 2

z score is positive indicating that the raw score is above the mean.

**Example 2:** Find the Z-score for a raw score of 8, mean 10, and standard deviation 2 and verify it using the z score calculator.

**Solution:**

Given raw score x = 8, mean \(\mu\) = 3 and standard deviation \(\sigma\) = 1

z = \(\frac{x - \mu }{\sigma }\) = (8 - 10)/2 = -1

z value is negative indicating that the raw score is below the mean.

Similarly, you can try the Z-score calculator to find the Z-score for the following:

- Find Z-score when raw score = 5, mean = 10 , standard deviation = 2
- Find Z-score when raw score = 20, mean = 15 , standard deviation = 5

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