now we've talked about how to find the standard deviation of a population but of course in real life it's often impractical or impossible to find all the data for a population that's why we sample a population right so what we would like to do is be able to find the standard deviation for a sample and the goal is we want the standard deviation of our sample to be a good approximation of the standard deviation of the population the best we could do anyway okay so let's first review what this looks like for a population and then we'll talk about how to find things for a sample so for a population and remember we have special symbols here so for a population the mean is Mu we add up all our data and divide by how many values there are in the population how much data is in the population which we notate by capital N okay in the sample it's almost the same we just switch out the symbols we use so in a sample we call the sample mean X bar that's how we say that we're dealing with the mean of a sample okay and we do the same thing that we add them up all the values in our sample we divide by how many there are we just denote the number of data values in our sample by little n instead in Step again okay so straightforward essentially the same formula we're just switching out some symbols forward standard deviation it's not quite so simple for population our standard deviation which we notate using the Greek letter Sigma we add up all our deviations x minus mu squared divide by how many there are okay that way we're averaging the squared distance of each data value from mu and then to correct for the square we take the square root well standard deviation is almost the same but it's not quite as simple as just for just changing out some symbols okay so the sample standard deviation we notate with a lowercase s and it starts off about the same we look at how far each data value is our in our sample is away from the sample mean okay we Square it to get rid of the direction information we just care about the distance and then instead of averaging it we still add them all up but instead of dividing by n we end up dividing by n minus 1. one less than the sample size okay and so that's a a pretty significant difference between the two formulas That's goes beyond just switching out the symbols and so it's going to be really important that you know when you're dealing with a sample and when you're dealing with a population okay because the formulas are different so why do we why is it different why do we have n minus 1 here instead of just n well remember what the goal is we want our sample standard deviation to be a good approximation for our population standard deviation our population standard deviation is a measure of the average distance of the data from the population mean mu what are we calculating over here we're calculating the distance of each state of value in the sample from the sample mean X bar now X bar should approximate mu but they're not the same thing so s isn't or or if we just had M here it wouldn't quite be the average data we wouldn't be approximating the average distance from mu we would be measuring the average distance from X bar and that's not what we want so to correct for that we throw in a minus one down here and it's a little bit complicated why that works if you're interested you could take a more advanced statistics course later on but it turns out that's the magic uh magic formula that will correct for that small error okay so that is our formula for our sample standard deviation in the next example we'll show how to calculate the standard deviation for a sample