# How do you find the standard deviation above the mean?

## How do you find the standard deviation above the mean?

Since the z-score is the number of standard deviations above the mean, z = (x – mu)/sigma. Solving for the data value, x, gives the formula x = z*sigma + mu. So the data value equals the z-score times the standard deviation, plus the mean.

**Is 1 standard deviation above the mean?**

For an approximately normal data set, the values within one standard deviation of the mean account for about 68% of the set; while within two standard deviations account for about 95%; and within three standard deviations account for about 99.7%.

**What is SD divided by mean?**

If you know nothing about the data other than the mean, one way to interpret the relative magnitude of the standard deviation is to divide it by the mean. This is called the coefficient of variation. For example, if the mean is 80 and standard deviation is 12, the cv = 12/80 = . 15 or 15%.

### What if the standard deviation is close to the mean?

Basically, a small standard deviation means that the values in a statistical data set are close to the mean (or average) of the data set, and a large standard deviation means that the values in the data set are farther away from the mean. The second data set isn’t better, it’s just less variable.

**Can mean and standard deviation be the same?**

There is no direct relationship between mean and SD because the mean is simple average of algebraic sum of data whereas the SD is obtained from the average of the square of data. Also SD is obtained by removing mean from the data. Statistically, there is no limit on SD with respect to mean.

**How do you compare two mean and standard deviation?**

How to compare two means when the groups have different standard deviations.

- Conclude that the populations are different.
- Transform your data.
- Ignore the result.
- Go back and rerun the t test, checking the option to do the Welch t test that allows for unequal variance.
- Use a permuation test.

#### Can standard deviation be higher than the mean?

Standard deviation (SD) can be higher than the mean. Note that SD, by definition, is always positive. However, mean can be positive or negative. For, example, if your variable has only negative values or has large proportion of negative values, the mean can be negative, in which case it is less than SD.

**What if the standard deviation is greater than mean?**

Standard deviation greater than the mean can happen even if the data are not skewed. Skew is a different descriptor of the shape of the distribution. Positive and negative values are not relevant. This condition can happen for any mix of positive and negative values including all values being positive. It can happen in real data without error.

**What does standard deviation actually tell me?**

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 close to the average, while a high standard deviation means that the numbers are more spread out.

## What is the difference between standard deviation and mean?

• Standard deviation is a measure of dispersion from the center, whereas mean measures the location of the center of a data set. • Standard deviation is always a nonnegative value, but mean can take any real value.