Answer:
10.94
Step-by-step explanation:
The standard deviation is calculated by using the following formula:
![s=\sqrt{\frac{1}{N-1}sum(xi -x)^2}](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B%5Cfrac%7B1%7D%7BN-1%7Dsum%28xi%20-x%29%5E2%7D)
This means that N is the total number of cases you want to take into account, times the sum of x at the ith position - x squared.
In other words, the standard deviation in your example implies the following:
26 is the first value, so i = 1, 34 is the second value, so i = 2, 18 where i = 3, and so on and so forth, until you reach the end, which is 6 (so the initial value is 1 and the last one is 6).
You're doing a sum over an iteration of all the numbers in your sample.
So applying the sum of all of the numbers, it gives us the following:
![(26-28)^2+(34 - 28)^2+(18 - 28)^2 ... (41 - 28)^2](https://tex.z-dn.net/?f=%2826-28%29%5E2%2B%2834%20-%2028%29%5E2%2B%2818%20-%2028%29%5E2%20...%20%2841%20-%2028%29%5E2)
![= \frac{598}{5} \\=119.6\\](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B598%7D%7B5%7D%20%5C%5C%3D119.6%5C%5C)
The sum of all of the numbers in your sample is equal to 119.6.
Substitute into the equation once again:
![s=\sqrt{119.6}](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B119.6%7D)
Where the square root of 119.6 is 10.93617...
Rounded to two decimal places: 10.94