# What is a high and low standard deviation?

## What is a high and low standard deviation?

A **low standard deviation** indicates that the data points tend to be very close to the mean. A **high standard deviation** indicates that the data points are spread out over a large range of values. ... The **standard deviation** is simply the square root of the variance.

## What would be considered a high standard deviation?

For an approximate answer, please estimate your coefficient of variation (CV=**standard deviation** / mean). As a rule of thumb, a CV >= 1 indicates a relatively **high** variation, while a CV < 1 can be **considered** low. ... A "**good**" **SD** depends if you expect your distribution to be centered or spread out around the mean.

## Why is standard deviation The square root of variance?

**Standard deviation** (S) = **square root** of the **variance** Because of its close links with the mean, **standard deviation** can be greatly affected if the mean gives a poor measure of central tendency. **Standard deviation** is also influenced by outliers one value could contribute largely to the results of the **standard deviation**.

## Why standard deviation is always positive?

The **standard deviation is always positive** precisely because of the agreed on convention you state - it measures a distance (either way) from the mean. But you're wrong about square roots. Every **positive** real number has two of them. but only the **positive** one is meant when you use the sign.

## Is variance always greater than standard deviation?

The point is for numbers > 1, the **variance** will **always** be **larger than** the **standard deviation**. **Standard deviation** has a very specific interpretation on a bell curve. **Variance** is a better measure of the "spread" of the data. ... But for values less **than** 1, the relationship between **variance** and **SD** becomes inverted.

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