To calculate the standard deviation of a set of data points, follow these steps:

1. Find the mean (average) of the data set.
2. Subtract the mean from each data point and square the result.
3. Find the mean of the squared differences.
4. Take the square root of the mean of squared differences to get the standard deviation.

Given the data set: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

1. Mean (\(\mu\)) = \(\frac{-5 - 4 - 3 - 2 - 1 + 0 + 1 + 2 + 3 + 4 + 5}{11} = 0\)

2. Squared differences:
  (-5 - 0)^2 = 25
  (-4 - 0)^2 = 16
  (-3 - 0)^2 = 9
  (-2 - 0)^2 = 4
  (-1 - 0)^2 = 1
  (0 - 0)^2 = 0
  (1 - 0)^2 = 1
  (2 - 0)^2 = 4
  (3 - 0)^2 = 9
  (4 - 0)^2 = 16
  (5 - 0)^2 = 25

3. Mean of squared differences = \(\frac{25 + 16 + 9 + 4 + 1 + 0 + 1 + 4 + 9 + 16 + 25}{11} = \frac{110}{11} = 10\)

4. Standard deviation (\(\sigma\)) = \(\sqrt{10}\)