>Hello Sohib EditorOnline! If you are looking for a way to calculate z-score, then you’ve come to the right place. In this article, we will explain what z-score is, how to calculate it, and its importance in statistics. So, let’s get started!

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## What is Z Score?

Z-score, also known as standard score, is a statistical measurement that tells you how many standard deviations a particular value is from the mean of a normal distribution. It is usually represented by the letter ‘z’.

Z-score is defined as:

z = (x – μ) / σ |

where:

- z is the z-score
- x is the value
- μ is the mean
- σ is the standard deviation

## How to Calculate Z Score?

Calculating z-score involves three steps:

### Step 1: Find the Mean and Standard Deviation

To calculate the z-score, you must first find the mean and standard deviation of the data set. The mean is the average value of the data set, and the standard deviation is a measure of how spread out the data is from the mean.

### Step 2: Determine the Value of Interest

The value of interest is the value whose z-score you want to calculate. It could be a data point in the data set or any value you want to measure against the distribution.

### Step 3: Calculate the Z Score

Once you have found the mean, standard deviation, and the value of interest, you can plug them into the z-score formula:

z = (x – μ) / σ |

Let’s take an example to understand this better.

## Example

Suppose you have a data set of test scores with a mean of 75 and a standard deviation of 10. You want to find the z-score for a score of 85.

### Step 1: Find the Mean and Standard Deviation

Mean = 75, Standard Deviation = 10

### Step 2: Determine the Value of Interest

Value of Interest = 85

### Step 3: Calculate the Z Score

z = (85 – 75) / 10 = 1

The z-score for a score of 85 is 1. This means that the score is one standard deviation above the mean.

## FAQ

### What does a positive or negative z-score mean?

A positive z-score means that the value is above the mean, and a negative z-score means that the value is below the mean.

### What is the importance of z-score?

Z-score is used in statistics to compare values from different normal distributions, and it helps to determine the probability of a given value occurring within a certain range.

### What is the range of z-score?

The range of z-score is from -3 to +3, where a z-score of -3 indicates that the value is three standard deviations below the mean, and a z-score of +3 indicates that the value is three standard deviations above the mean.

### Can z-score be negative?

Yes, z-score can be negative if the value is below the mean.

### What is the difference between z-score and t-score?

The main difference between z-score and t-score is that z-score is used when the sample size is large, and the population standard deviation is known, whereas t-score is used when the sample size is small, and the population standard deviation is unknown.

## Conclusion

In summary, z-score is a statistical measurement that tells you how many standard deviations a particular value is from the mean of a normal distribution. Calculating z-score involves finding the mean and standard deviation of the data set and plugging them into the z-score formula. Z-score is important in statistics and helps to determine the probability of a given value occurring within a certain range. We hope this article has helped you understand how to calculate z-score.