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##### Asked by: Yaeko Inderdohnen

science physics# How do you find the proportion of one standard deviation?

Last Updated: 17th January, 2020

**a**normaldistribution's values are within

**one standarddeviation**ofthe mean. 95% are within two

**standarddeviations**and 99.7%are within three

**standarddeviations**. That means that the

**proportion**of valueswithin

**one standard deviation**is68/100 = 17/25.

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Similarly one may ask, how do you find the percentage of one standard deviation?

The Empirical Rule or 68-95-99.7% Rule can give us agoodstarting point. This rule tells us that around 68% of the datawillfall **within** one **standard deviation** of the mean;around95% will fall **within** two **standard deviations**of themean; and 99.7% will fall **within** three**standarddeviations** of the mean.

Secondly, what percentage of the data is within 2 standard deviations of the mean? For a **data** set with a symmetric distribution,approximately 68.3 **percent** of the values willfall**within** one **standard deviation** from the**mean**,approximately 95.4 **percent** will fall **within 2standarddeviations** from the **mean**, and approximately99.7**percent** will fall **within** 3 **standarddeviations**from the **mean**.

Also, how do you find the standard deviation of a sample size?

**First, let's review the steps for calculating thesamplestandard deviation:**

- Calculate the mean (simple average of the numbers).
- For each number: subtract the mean.
- Add up all of the squared results.
- Divide this sum by one less than the number of data points (N-1).

What is the formula for standard deviation?

The **standard deviation** is given bythe**formula**: s means '**standard deviation**'. Now,subtractthe mean individually from each of the numbers given andsquare theresult. This is equivalent to the (x - )²step.