Simple Example of Calculating Standard Deviation

Let's say we wanted to calculate the standard deviation for the amounts of gold coins pirates on a pirate ship have.

There are 100 pirates on the ship. In statistical terms this means we have a population of 100. If we know the amount of gold coins each of the 100 pirates have, we use the standard deviation equation for an entire population:

What if we don't know the amount of gold coins each of the 100 pirates have? For example, we only had enough time to ask 5 pirates how many gold coins they have. In statistical terms this means we have a sample size of 5 and in this case we use the standard deviation equation for a sample of a population:

The rest of this example will be done in the case where we have a sample size of 5 pirates, therefore we will be using the standard deviation equation for a sample of a population.

Here are the amounts of gold coins the 5 pirates have:

4, 2, 5, 8, 6.

Now, let's calculate the standard deviation:

1. Calculate the mean: