## 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:

2. Calculate for each value in the sample:

3. Calculate :

4. Calculate the standard deviation:

**The standard deviation for the amounts of gold coins the pirates have is 2.24 gold coins. **

See also:

Standard Deviation Wiki

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