What does the mean and standard deviation tell you?
Standard deviation is a number used to tell how measurements for a group are spread out from the average (mean), or expected value. A low standard deviation means that most of the numbers are very close to the average. A high standard deviation means that the numbers are spread out.
In statistics, the 68–95–99.7 rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard
- If the population distribution is Normal then: 68% of the population is within 1 standard deviation of the mean. 95% of the population is within 2 standard deviations of the mean. 99% of the population is within 2 1/2 standard deviations of the mean.
- If a data distribution is approximately normal then about 68 percent of the data values are within one standard deviation of the mean (mathematically, μ ± σ, where μ is the arithmetic mean), about 95 percent are within two standard deviations (μ ± 2σ), and about 99.7 percent lie within three standard deviations (μ ± 3σ
- Three-sigma limit (3-sigma limits) is a statistical calculation that refers to data within three standard deviations from a mean. Control charts are used to establish limits for a manufacturing or business process that is in a state of statistical control.
In any normal distribution with mean μ and standard deviation σ : Approximately 68% of the data fall within one standard deviation of the mean. Approximately 95% of the data fall within two standard deviations of the mean. Approximately 99.7% of the data fall within three standard deviations of the mean.
- To calculate the standard deviation of those numbers:
- Work out the Mean (the simple average of the numbers)
- Then for each number: subtract the Mean and square the result.
- Then work out the mean of those squared differences.
- Take the square root of that and we are done!
- Confidence Intervals
Desired Confidence Interval Z Score 90% 95% 99% 1.645 1.96 2.576
- To find the Z score of a sample, you'll need to find the mean, variance and standard deviation of the sample. To calculate the z-score, you will find the difference between a value in the sample and the mean, and divide it by the standard deviation.
Updated: 2nd October 2019