For a given set of data, which of these is always the largest?

In this scenario, the largest measure from the given choices is the population variance. Understanding the relationship between variance and standard deviation is key here.

Variance measures the average of the squared differences from the mean, and while standard deviation is simply the square root of variance, it will always be smaller in value since it fundamentally represents the same data in a different form. Specifically, for any set of data, the population variance is calculated by taking the average of the squared deviations from the mean and will yield a larger numerical value than the standard deviation, which is derived from that variance.

Likewise, the sample variance, while also being a measure of spread but calculated differently when dealing with a sample from a larger population, will follow the same principle: the variance itself is larger than the square root form of that value, which would be the sample standard deviation.

Therefore, population variance is the correct answer as it consistently yields the highest numerical value among the set of options.