Dataset's Standard Deviation

This statistics interview question uses a very small, evenly spaced dataset of consecutive integers to test understanding of how dispersion is quantified. The candidate is asked to compute the standard deviation and, more importantly, to interpret what exactly is being measured. Because the data are simple and symmetric, mental arithmetic is usually enough, making it a common warm-up in quantitative interviews or basic data analysis screenings. The twist is not the arithmetic itself, but recognizing what assumption is being made about the dataset: is it being treated as the entire population or as a sample drawn from something larger?

To answer correctly, the candidate must recall and apply the correct variance and standard deviation formulas, including the appropriate denominator. The problem leans on comfort with means, squared deviations, and square roots, and on not conflating population and sample formulas. Interviewers watch for whether the candidate states their assumption clearly, manipulates the small numbers accurately, and shows awareness of why the denominator choice matters for statistical inference.

What it tests

Standard deviation measures the spread of data around the mean, but the precise formula depends on whether the data represents a complete `population` or a `sample` from a larger set. For a population, the variance is the mean of squared deviations from the mean, dividing by $N$, the total number of data points. For a sample, the variance divides by $N-1$ (Bessel's correction) to correct for the bias in estimating the population variance from a finite sample. This correction arises because the sample mean itself is a random variable that tends to be closer to the sample points than the true population mean, so dividing by $N$ would systematically underestimate the variance. The key is recognizing that the context (sample vs. population) determines the denominator and thus the final value for standard deviation.