# What does it mean to be within one standard deviation?

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**A.

### What does the standard deviation tell you about the data?

**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.

#### Is variance and standard deviation the same?

The**standard deviation**is the square root of the**variance**. The**standard deviation**is expressed in the same units as the mean is, whereas the**variance**is expressed in squared units, but for looking at a distribution, you can use either just so long as you are clear about what you are using.#### Can you get a negative standard deviation?

The**standard deviation can**never be**negative**– squaring all**deviations**results in a list of all positive numbers. ______5. Squaring every number in a list will square both the mean and the SD.#### What is a standard deviation for dummies?

The**standard deviation**is a measurement statisticians use for the amount of variability (or spread) among the numbers in a data set. As the term implies, a**standard deviation**is a**standard**(or**typical**) amount of**deviation**(or distance) from the average (or mean, as statisticians like to call it).

B.

### What does it mean if you have a standard deviation of 0?

This

**means**that for every i, the term (x_{i}- x )^{2}=**0**. This**means**that every data value**is**equal to the**mean**. This result along with the one above allows us to say that the sample**standard deviation**of a data set**is**zero**if**and only**if**all of its values are identical.#### Is the standard deviation resistant?

The IQR is a type of**resistant**measure. The second measure of spread or variation is called the**standard deviation**(SD). The**standard deviation**is calculated using every observation in the data set. Consequently it is called a sensitive measure because it will be influenced by outliers.#### Is a standard deviation always a positive number?

No,**standard deviation**is**always positive**or 0. When you square**deviations**from the mean, they become**positive**or zero. Their sum is still**positive**or zero and the quotient after dividing the sum by n – 1 stays**positive**or zero. This final quantity is the variance.#### Can variance be zero?

**Variance**is non-negative because the squares are positive or**zero**: The**variance**of a constant random variable is**zero**, and if the**variance**of a variable in a data set is 0, then all the entries have the same value: In general we have for the sum of random variables.

C.

### Can standard deviation be less than 1?

A smaller

**standard deviation**indicates that**more**of the data is clustered about the mean. A larger**one**indicates the data are**more**spread out. In the first case, the**standard deviation**is**greater than**the mean. In the second case, it is smaller.#### What are the characteristics of a normal distribution of data?

Here, we see the four**characteristics**of a**normal distribution**.**Normal distributions**are symmetric, unimodal, and asymptotic, and the mean, median, and mode are all equal. A**normal distribution**is perfectly symmetrical around its center. That is, the right side of the center is a mirror image of the left side.#### What does it mean to have a higher standard deviation?

A low**standard deviation**indicates that the data points tend to be close to the**mean**(also called the expected value) of the set, while a**high standard deviation**indicates that the data points are spread out over a wider range of values.#### What does it mean to have a low standard error?

The**standard error is the**estimated**standard**deviation or measure of variability in the sampling distribution of a statistic. A**low standard error**means there is relatively less spread in the sampling distribution. The**standard error**indicates the likely accuracy of the sample**mean**as compared with the population**mean**.

Updated: 2nd October 2019