Question

What is the standard deviation of {77, 26, 41, 26, 84, 21}?

Answer 1

The standard deviation is approximately 27.766 units.

Explanation:

To determine this, we must first find the arithmetic mean of the data set. This is determined below:

`bar x = (sum _(i=1) ^n x_i)/n = 275/6 = 45.833`

With this in mind, we can now look at the standard deviation. The standard deviation `s` is defined thusly:

`s = sqrt (((sum _(i=1) ^n x_i^2) - nbarx^2)/(n-1))`

With `n=6, barx = 45.833, barx^2 = 2100.694444,` and our values for the various `x_i`, we obtain:

`s approx 27.766`