# What does the mean and standard deviation tell us?

**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 the difference between the mean and the standard deviation?

The

**standard deviation**is simply the square root of the variance. The**average deviation**, also called the**mean**absolute**deviation**, is another measure of variability. However,**average deviation**utilizes absolute values instead of squares to circumvent the issue of negative**differences between**data and the**mean**.#### What is the deviation from the mean?

The**average**of these numbers (6 ÷ 5) is 1.2 which is the**mean deviation**. Also called**mean**absolute**deviation**, it is used as a measure of dispersion where the number of values or quantities is small, otherwise standard**deviation**is used.#### What percentage is within one standard deviation of the mean?

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#### What does SD mean in a study?

The Normal Curve tells us that numerical data will be distributed in a pattern around an average (the center line).**Standard deviation**is considered the most useful index of variability. It is a single number that tells us the variability, or spread, of a distribution (group of scores).

B.

### What is standard deviation in math?

The

**Standard Deviation**is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma) The**formula**is easy: it is the square root of the Variance.#### What does the standard deviation measure?

For a given data set, the**standard deviation measures**how spread out numbers are from an average value.**Standard deviation**can be calculated by taking the square root of the variance, which itself is the average of the squared differences of the mean.#### What is the formula for variance and standard deviation?

The**variance**(symbolized by S^{2}) and**standard deviation**(the square root of the**variance**, symbolized by S) are the most commonly used measures of spread. We know that**variance**is a measure of how spread out a data set is. It is calculated as the average squared**deviation**of each number from the mean of a data set.#### What does S mean in statistics?

By convention, specific symbols represent certain sample**statistics**. For example, x refers to a sample mean.**s**refers to the standard deviation of a sample.**s**^{2}refers to the variance of a sample.

Updated: 2nd October 2019