# How do you find the standard deviation for the numbers 4, 4, 5, 5, 6, 6?

Jun 4, 2017

Standard Deviation $\approx$0.816

#### Explanation:

There are 4 steps to find the standard deviation:
1. Work out the Mean of the given set of numbers
2. Then for each number: subtract the Mean and square the result
3. Then work out the mean of those squared differences.
4. Take the square root of that and we are done!

Step 1: To find the mean for any given set of numbers, you add all of the numbers together, and divide that sum by how many numbers
there were. For example, if you have the numbers (4,4,5,5,6,6), you would first add them all together (4+4+5+5+6+6=30), then divide the answer by how many numbers there were (#30/6=5).

Step 2: Now we subtract the mean (5) from each number, and square the result, which looks like: (${\left(4 - 5\right)}^{2} = 1$), (${\left(4 - 5\right)}^{2} = 1$),
(${\left(5 - 5\right)}^{2} = 0$), (${\left(5 - 5\right)}^{2} = 0$), (${\left(6 - 5\right)}^{2} = 1$) and (${\left(6 - 5\right)}^{2} = 1$).

Step 3: Now we add all the new answers together ($1 + 1 + 0 + 0 + 1 + 1 = 4$), and then divide them by how many new answers there were $\frac{4}{6} = \frac{2}{3}$.

Step 4: For the last step, we take the square root of the answer from step 3, which equals $\sqrt{\frac{2}{3}} \approx 0.816$

Thus 0.816 becomes the standard deviation,
I hope that helped!