# 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.
A.

### What is 3 standard deviations?

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
• #### How many standard deviation is 99%?

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.
• #### What does 3 standard deviations 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
• #### What is 3 sigma limits?

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.
B.

### What percentage of the data falls within 2 standard deviation of the mean?

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.
• #### How do you calculate the standard deviation?

To calculate the standard deviation of those numbers:
1. Work out the Mean (the simple average of the numbers)
2. Then for each number: subtract the Mean and square the result.
3. Then work out the mean of those squared differences.
4. Take the square root of that and we are done!
• #### What is the Z Star for a 90 confidence interval?

Confidence Intervals
Desired Confidence IntervalZ Score
90% 95% 99%1.645 1.96 2.576
• #### How do you find the Z score?

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: 3rd December 2019