Standard deviation

For a sample of $n$ observations we call the numbers

$$x_1, x_2, \ldots x_n$$

Web resources:
as explained to journalists
With a formula

Statistics at Square One

Quick and easy guess

We can study the following quantitites: Deviation from the mean.
Absolute deviation from the mean
Average absolute deviation.
Standard deviation.

Here is the example I did in class:
Sinus measurements in mm:

42 27 25 40 33 31 42 34 35 25 29 30 29 35

   2 : 55799
   3 : 0134
   3 : 55
   4 : 022

$$\bar{x}=32.642$$

Here are the deviations to the mean:

9.4 -5.6 -7.6 7.4 0.4 -1.6 9.4  1.4 2.4 -7.6 -3.6 -2.6 -3.6 2.4

I remarked that

$$\sum (x_i-\bar{x})=0$$

(You should check this with your calculator)

Here are the squares of the deviations:

$$(x_i-\bar{x})^2$$

87.6 31.8 58.4 54.1 0.1 2.7 87.6 1.8 5.6 58.4 13.3 7 13.3 5.6

$$\hat{\sigma}^2=\frac{\sum(x_i-\bar{x})^2}{n}=\frac{427.2}{14}=30.5$$

$$\hat{\sigma}=\sqrt{30.5}= 5.5$$

Algorithm for computing the standard deviation

1. Compute the mean.
2. Deviations from the mean.
3. Squares of the deviations.
4. Average of the squares of the deviation.
5. Square root of the average of the squares of the deviations.