Final answer:
A z-score can be either positive or negative; a positive z-score means the data point is above the mean, while a negative z-score indicates it is below the mean. The magnitude indicates how far away the data point is from the mean.
Step-by-step explanation:
The standardized value referred to in the question is also known as the z-score in statistics. A z-score can be either positive or negative, indicating the position of a data point in relation to the mean of the data set. When z is positive, it means that the data point is above or to the right of the mean. Conversely, when z is negative, the data point is below or to the left of the mean. The absolute value of z indicates the distance of the data point from the mean, regardless of the direction.
It is important to understand that a z-score reflects the number of standard deviations a data point is from the mean. Since standard deviation cannot be negative, the z-score's sign merely indicates the direction from the mean, and the magnitude represents how unusual or typical the data point is compared to the rest of the data.