Here is the procedure for calculating the standard deviation by hand or "by hand" using a spreadsheet.

1. Find the mean of all the data in the sample ( ).

2. Find the distance of each data point from the sample mean ( xi – )

3. Square each distance.

4. Add up all the squares.

5. Divide this sum by the number of data points minus one (n-1). This is the "average" part.

6. Take the square root of the result.

This statistic is s, the sample standard deviation. It is an estimate of .

The table below shows a calculation of the standard deviation of the line1 package weights.
Note that values far from the mean (13 and 17) contribute greatly to the standard deviation.

Line 1 net wts.	Distance from mean	Squared distance
13	-1.5	2.25
13	-1.5	2.25
14	-0.5	0.25
14	-0.5	0.25
14	-0.5	0.25
14	-0.5	0.25
15	0.5	0.25
15	0.5	0.25
17	2.5	6.25
mean = 14.5		sum of squares = 12.25
		n-1 mean of squares = 12.25 / 9 = 1.361
		sq. root of 1.361 = 1.17 = s

#20 Calculate the standard deviation of the line 2 package weights. The standard deviation for line 2 is higher at 1.84, reflecting the greater spread of the data from the mean.

Standard deviation is always in the same units as the original data. For example, the standard deviation of women's heights, measured in inches, is about 2.5 inches.