Can Z Score be Negative

Yes, Z-Score can be negative. The negative z score value represents the raw score value that is either left or below the mean of the standard normal distribution.

The Z-score value can be negative, positive, or 0. If the z score value is negative, use the negative z-score table chart to find the area. It shows the area under the curve of normal distribution.

The Z-score can be calculated using the either z-score formula or the z-score calculator.

To calculate the z-score using the formula, use the below z-score formula

z = (x -μ )/σ

Where: μ = is the population mean for the unstandardized value σ = is the population standard deviation for the unstandardized value x = is the raw score value

z = is the calculated z-score value.

In this tutorial, we will discuss the negative z-score with an example.

Negative Z Score Value

Let’s consider the example below to find the z-score.

Consider, we have below information

• Mean: 78
• Standard deviation: 4
• Raw score: 69

To find the z-score, use below z-score formula.

z = (x – μ )/σ

Use the input parameters in the z-score formula

z = (69-78)/4

z = -2.25

The z-score for the raw score 69 is -2.25. This means that the raw score of 69 is a 2.25 standard deviation below the mean of 78.

In the above example, the Z-score value is negative, hence we will use the negative z score table to find the area.

Conclusion

I hope the above article is helpful to understand z-score value can be negative. A negative z-score value represents your raw score value is less than the mean of normal distribution.

You can find more topics about Z-Score and how to calculate the z score given the area on the ZscoreGeek home page.