A standard deviation of 3” means that most men (about 68%, assuming a normal distribution) have a height 3″ taller to 3” shorter than the average (67″–73″) — one standard deviation. Three standard deviations include all the numbers for 99.7% of the sample population being studied.

Discrete variables

1. Calculate the mean.
2. Subtract the mean from each observation.
3. Square each of the resulting observations.
4. Add these squared results together.
5. Divide this total by the number of observations (variance, S2).
6. Use the positive square root (standard deviation, S).

An Example of Calculating Three-Sigma Limit

1. First, calculate the mean of the observed data.
2. Second, calculate the variance of the set.
3. Third, calculate the standard deviation, which is simply the square root of the variance.
4. Fourth, calculate three-sigma, which is three standard deviations above the mean.

Key Takeaways. The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.

For an approximately normal data set, the values within one standard deviation of the mean account for about 68% of the set; while within two standard deviations account for about 95%; and within three standard deviations account for about 99.7%.

When stocks are following a normal distribution pattern, their individual values will place either one standard deviation below or above the mean at least 68% of the time. A stock’s value will fall within two standard deviations, above or below, at least 95% of the time.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

The higher the standard deviation, the riskier the investment. On the other hand, the larger the variance and standard deviation, the more volatile a security. While investors can assume price remains within two standard deviations of the mean 95% of the time, this can still be a very large range.

Standard deviation is a mathematical tool to help us assess how far the values are spread above and below the mean. A high standard deviation shows that the data is widely spread (less reliable) and a low standard deviation shows that the data are clustered closely around the mean (more reliable).

Distributions with a coefficient of variation to be less than 1 are considered to be low-variance, whereas those with a CV higher than 1 are considered to be high variance.

What are acceptable variances? The only answer that can be given to this question is, “It all depends.” If you are doing a well-defined construction job, the variances can be in the range of ± 3–5 percent. If the job is research and development, acceptable variances increase generally to around ± 10–15 percent.

A large variance indicates that numbers in the set are far from the mean and far from each other. A variance value of zero, though, indicates that all values within a set of numbers are identical. Every variance that isn’t zero is a positive number. A variance cannot be negative.

The coefficient of variation (CV) is the ratio of the standard deviation to the mean. The higher the coefficient of variation, the greater the level of dispersion around the mean. It is generally expressed as a percentage. The lower the value of the coefficient of variation, the more precise the estimate. …

Basically CV<10 is very good, 10-20 is good, 20-30 is acceptable, and CV>30 is not acceptable.

Variance: The variance is just the square of the SD. Coefficient of variation: The coefficient of variation (CV) is the SD divided by the mean. For the IQ example, CV = 14.4/98.3 = 0.1465, or 14.65 percent.

The point is for numbers > 1, the variance will always be larger than the standard deviation. Standard deviation has a very specific interpretation on a bell curve. Variance is a better measure of the “spread” of the data. But for values less than 1, the relationship between variance and SD becomes inverted.

The coefficient of variation shows the extent of variability of data in a sample in relation to the mean of the population. In finance, the coefficient of variation allows investors to determine how much volatility, or risk, is assumed in comparison to the amount of return expected from investments.

RSD also is known as the coefficient of variation (CV). By definition standard deviation is a quantity calculated to indicate the extent of deviation for a group as a whole.

You can also use standard deviation to compare two sets of data. For example, a weather reporter is analyzing the high temperature forecasted for two different cities. A low standard deviation would show a reliable weather forecast.