# 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:**- 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!

#### What is the Z Star for a 90 confidence interval?

Confidence IntervalsDesired Confidence Interval Z 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: 2nd October 2019