What is the standard deviation of the numbers 1, 2, 3, 4, 5?

To find the standard deviation of the numbers (1, 2, 3, 4, 5), we first need to calculate the mean (average) of the numbers. The mean is given by:

[

\text{Mean} = \frac{1 + 2 + 3 + 4 + 5}{5} = \frac{15}{5} = 3

]

Next, we find the variance, which is the average of the squared differences from the mean. We will calculate each squared difference:

• For (1): ((1 - 3)^2 = (-2)^2 = 4)

• For (2): ((2 - 3)^2 = (-1)^2 = 1)

• For (3): ((3 - 3)^2 = (0)^2 = 0)

• For (4): ((4 - 3)^2 = (1)^2 = 1)

• For (5): ((5 - 3)^2 = (2)^2 = 4)

Now, we sum these squared differences:

[

4 + 1 + 0 +