How To Calculate Standard Error

Hi I'm Peter Edwards from Blue Tutors. We teach children of all ages right from primary school to degree level and we find the highest quality tutors. And today, I'm going to teach you some Maths.

So now we're going to look at how to calculate the standard error - which is sometimes often called the standard deviation of a set of data. So it's a statistical calculation to work out the spread of the data. So, basically we work out the mean first, and from that we can see how much the data has spread around the mean.

So, we have this equation here, which is the standard error. We're going to call it sigma, and we're squaring it for the purposes of this. It's the sum of the data, minus the value of the mean, and you square each time you do that.

And then you divide it by the number of pieces of data that you have. So we're going to do an example with this data first hopefully to give you an idea of how to work out, well, the mean is probably the most important part. So, how do you work out the mean of this data? Well, we add all of them together and we divide by the number of data points we have.

And that is fifteen over five, which is equal to three. And we can fairly obviously see that from here three is in the middle of them anyway. So, we now have the mean, which is three and we're now going to do this calculation up here so, the standard error squared is equal to the sum, that's what that symbol means it just means the sum of each of these points of one minus three squared plus two minus three squared plus three minus three squared plus four minus three squared plus five minus three squared.

And we're going to divide all of that by the number of points we have which is five. So this is two squared plus one squared plus zero squared plus one squared plus two squared over five which is ten over five which is equal to two. So that's our sigma squared, so sigma is going to equal the square route of two which is roughly one point one for one which us an idea about how much this data is spread.

That's what the standard error is a measure of, it's a measure of the spread of the data. And so that's how to calculate the standard error. .