Final answer:
The z-score for a given data value represents the number of standard deviations a data point is from the mean of the distribution.
Step-by-step explanation:
To compute the z-score for a given data value, use the formula: z = (x - μ) / σ, where x is the data value, μ is the mean of the distribution, and σ is the standard deviation. This z-score helps in understanding the relative position of a particular data point in relation to the mean and provides insights into how extreme or typical that value is within the dataset.
For example, if a z-score is negative, it indicates that the data point is below the mean. A z-score of zero means the data point is exactly at the mean, and a positive z-score signifies that the data point is above the mean. The magnitude of the z-score indicates how far away the data point is from the mean in terms of standard deviations.
Interpreting the z-score involves understanding how unusual or common a data point is in comparison to the rest of the dataset. For instance, a z-score of 2 suggests that the data point is two standard deviations above the mean, indicating it's relatively far from the average and could be considered an outlier or an extreme value within the dataset. Conversely, a z-score close to zero implies the data point is closer to the mean and is more typical within the distribution.