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
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.
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.