Calculating Standard Deviation

The mathematical formula is as follows:

We'll go through this step by step so don't be put off if it looks horrendous.

Running through the meaning of the signs, the lower case sigma, σ, indicates Standard Deviation. The sign means square root. Upper case sigma, denoted by &Sigma, means "the sum of". x is each number in the data sample, and x-bar, denoted by the sign is the average (also known as the "mean") of the data set. n is simply the number of values in the data sample

As with most stock analysis tools, a period of time needs to be decided upon for the sample of data. For an example, we'll use 10 days worth of data. This will give the value of n as 10. We'll be calculating the 10 day Standard Deviation for the UK company, Royal Bank of Scotland Group PLC, at the close of trade on 14 December 2004. The prices for the 10 trading days up to and including the 14 December 2004 were:

Date in December 2004	1st	2nd	3rd	6th	7th	8th	9th	10th	13th	14th
Closing price (uk pence). These are the x values.	1,645.56	1,663.68	1,671.00	1,667.00	1,655.08	1,643.00	1,670.97	1,678.00	1,711.82	1,700.24
x-	-25.075	-6.955	0.365	-3.635	-15.555	-27.635	0.335	7.365	41.185	29.605
	628.755625	48.372025	0.133225	13.213225	241.958025	763.693225	0.112225	54.243225	1696.204225	876.456025

The average is (1,645.56+1,663.68+1,671.00+1,667.00+1,655.08+1,643.00+1,670.97+1,678.00+1,711.82+1,700.24) ÷ 10, which equals 1670.635. This figure of 1670.635 is our xbar (that is to say, our ) value. For each of our closing prices, these being our x values, we deduct the value to give (x- ), which is shown on the third row of the table above. Each (x- ) value is then squared (ie multiplied by itself) to find the values in the fourth column. We then need to add all of these values together to give the value. In our case, this is 628.755625 + 48.372025 + 0.133225 + 13.213225 + 241.958025 + 763.693225 + 0.112225 + 54.243225 + 1696.204225 + 876.456025, which equals 1354.52175.