# Which is better high or low standard deviation?

## Which is better high or low standard deviation?

A **high standard deviation** shows that the data is widely spread (less reliable) and a **low standard deviation** shows that the data are clustered closely around the mean (more reliable).

## What value is a high standard deviation?

there is no **value** that is "**high**." In one application I might expect a **standard deviation** that is close to zero no matter what the mean is.

## What is a large standard deviation?

A low **standard deviation** indicates that the values tend to be close to the mean (also called the expected value) of the set, while a **high standard deviation** indicates that the values are spread out over a wider range.

## How do you increase standard deviation?

If every term is doubled, the distance between each term and the mean doubles, BUT also the distance between each term doubles and thus **standard deviation** increases. If each term is divided by two, the **SD** decreases. (b) Adding a number to the set such that the number is very close to the mean generally reduces the **SD**.

## What does a low standard deviation mean?

**Low standard deviation means** data are clustered around the **mean**, and high **standard deviation** indicates data are more spread out. A **standard deviation** close to zero indicates that data points are close to the **mean**, whereas a high or **low standard deviation** indicates data points are respectively above or below the **mean**.

## How does changing the mean affect standard deviation?

When adding or subtracting a constant from a distribution, the **mean** will **change** by the same amount as the constant. The **standard deviation** will remain unchanged. This fact is true because, again, we are just shifting the distribution up or down the scale. We **do** not **affect** the distance between values.

## What happens to the mean and standard deviation when the sample size decreases?

The **mean** of the **sample means** is always approximately the same as the population **mean** µ = 3,500. Spread: The spread is smaller for larger **samples**, so the **standard deviation** of the **sample means decreases** as **sample size** increases.

## Should I report standard error or standard deviation?

So, if we want to say how widely scattered some measurements are, we use the **standard deviation**. If we want to indicate the uncertainty around the estimate of the mean measurement, we quote the **standard error** of the mean. The **standard error** is most useful as a means of calculating a confidence interval.

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