 # Question: Can A Standard Deviation Be Less Than 1?

## What does a standard deviation of 2 mean?

Specifically, if a set of data is normally (randomly, for our purposes) distributed about its mean, then about 2/3 of the data values will lie within 1 standard deviation of the mean value, and about 95/100 of the data values will lie within 2 standard deviations of the mean value.

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## Why is the mean 0 and the standard deviation 1?

The mean of 0 and standard deviation of 1 usually applies to the standard normal distribution, often called the bell curve. The most likely value is the mean and it falls off as you get farther away. … The simple answer for z-scores is that they are your scores scaled as if your mean were 0 and standard deviation were 1.

## How do you interpret a standard deviation?

More precisely, it is a measure of the average distance between the values of the data in the set and the mean. 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.

## Can you have a standard deviation greater than 1?

The answer is yes. (1) Both the population or sample MEAN can be negative or non-negative while the SD must be a non-negative real number. A smaller standard deviation indicates that more of the data is clustered about the mean while A larger one indicates the data are more spread out.

## What is considered a low standard deviation?

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.

## What does it mean to have a standard deviation of 1?

A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. Areas of the normal distribution are often represented by tables of the standard normal distribution. … For example, a Z of -2.5 represents a value 2.5 standard deviations below the mean.

## What does a standard deviation of 0.5 mean?

To understand standard deviation we need to look at mean first. Mean is more of a location parameter, where our data points lie on average. … So, a standard deviation of 0.5 basically means that on average the difference between mean and data points is 0.5.

## What does it mean if standard deviation is less than 1?

If my standard deviation and variance are above 1, the standard deviation will be smaller than the variance. But if they are below 1, the standard deviation will be bigger than the variance. … So you can’t say that the variance is bigger than or smaller than the standard deviation. They’re not comparable at all.

## Is standard deviation always less than 1?

Even when the mean is positive, it can be less than standard deviation. … One standard deviation to the right from the mean, for example, contains about 34% of of the values within the distribution. The mean, on the other hand, is a measure of the average value in your distribution.

## Is a standard deviation of 3 high?

A standard deviation of 3” means that most men (about 68%, assuming a normal distribution) have a height 3″ taller to 3” shorter than the average (67″–73″) — one standard deviation. Almost all men (about 95%) have a height 6” taller to 6” shorter than the average (64″–76″) — two standard deviations.

## How do you interpret standard deviation and standard error?

Standard Deviation: The Difference. The standard deviation (SD) measures the amount of variability, or dispersion, from the individual data values to the mean, while the standard error of the mean (SEM) measures how far the sample mean (average) of the data is likely to be from the true population mean.

## How much standard deviation is acceptable?

Statisticians have determined that values no greater than plus or minus 2 SD represent measurements that are more closely near the true value than those that fall in the area greater than ± 2SD. Thus, most QC programs call for action should data routinely fall outside of the ±2SD range.