What information does the z-score provide about a data point?

The z-score is a statistical measurement that indicates how many standard deviations a particular data point is from the mean of the dataset. This metric offers valuable insights into the position of that data point relative to the average value in the dataset. Specifically, a z-score of zero signifies that the data point is identical to the mean, while positive z-scores indicate that the point is above the mean and negative z-scores indicate that it is below the mean. This comparison to the mean is essential for understanding the relative standing of the data point within the overall distribution, which can help identify outliers and assess the data's distribution characteristics.

The other options, while they represent important statistical concepts, do not accurately reflect the function of the z-score. The average value of a dataset is not determined by the z-score itself, and the z-score does not provide the exact value of a data point in terms of the population; rather, it standardizes the score relative to the population mean and standard deviation. Lastly, the variance of the population data is a measure of how much the data points spread out from the mean, which is unrelated to the z-score's specific role in indicating relative position.