Why is n 1 in the denominator of s2

It only makes sense to use n in the denominator when there is no sampling from a population, there is no desire to make general conclusions. The goal of science is always to generalize, so the equation with n in the denominator should not be used. The only example I can think of where it might make sense is in quantifying the variation among exam scores.

But much better would be to show a scatterplot of every score, or a frequency distribution histogram. Analyze, graph and present your scientific work easily with GraphPad Prism. No coding required. Home Support. How ito calculate the standard deviation 1. However, while the sample mean is an unbiased estimator of the population mean, the same is not true for the sample variance if it is calculated in the same manner as the population variance.

If one took all possible samples of n members and calculated the sample variance of each combination using n in the denominator and averaged the results, the value would not be equal to the true value of the population variance; that is, it would be biased. This bias can be corrected by using n - 1 in the denominator instead of just n , in which case the sample variance becomes an unbiased estimator of the population variance. Standard deviation and variance are commonly used measures of dispersion.

If the sample variance is larger than there is a greater chance that it captures the true population variance. Because we are trying to reveal information about a population by calculating the variance from a sample set we probably do not want to underestimate the variance. There was a good post here on CV that will give you some good insight. Hope this helps! Sign up to join this community. The best answers are voted up and rise to the top.

Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. And when you divide by a smaller number, you're going to get a larger value. So this is going to be larger. This is going to be smaller. And this one, we refer to the unbiased estimate. And this one, we refer to the biased estimate. If people just write this, they're talking about the sample variance.

It's a good idea to clarify which one they're talking about. But if you had to guess and people give you no further information, they're probably talking about the unbiased estimate of the variance. So you'd probably divide by n minus 1.

But let's think about why this estimate would be biased and why we might want to have an estimate like that is larger. And then maybe in the future, we could have a computer program or something that really makes us feel better, that dividing by n minus 1 gives us a better estimate of the true population variance. So let's imagine all the data in a population. And I'm just going to plot them on number a line.

So this is my number line. This is my number line. And let me plot all the data points in my population. So this is some data. This is some data. Here's some data. And here is some data here. And I can just do as many points as I want.

So these are just points on the number line. Now, let's say I take a sample of this. So this is my entire population. So let's see how many. I have 1 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, So in this case, what would be my big N? My big N would be Big N would be