Contents

## Is the standard deviation or the coefficient of variation the better measure?

When you have hug differences in means and want to compare their variation, it would be better to take the coefficient of variation, because it normalizes the standard deviation with respect to the mean.

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

The coefficient of variation (CV) is a measure of relative variability. It is the ratio of the standard deviation to the mean (average). For example, the expression The standard deviation is 15% of the mean is a CV.

**When should standard deviation not be used?**

The standard deviation is used in conjunction with the mean to summarise continuous data, not categorical data. In addition, the standard deviation, like the mean, is normally only appropriate when the continuous data is not significantly skewed or has outliers.

**How do you know when to use population or sample standard deviation?**

The population standard deviation is a parameter, which is a fixed value calculated from every individual in the population. A sample standard deviation is a statistic. This means that it is calculated from only some of the individuals in a population.

### What is acceptable 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 SD depends if you expect your distribution to be centered or spread out around the mean.

### What is considered a good standard deviation?

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.

**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.

**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.

#### What does a standard deviation of 0 indicate?

When you square a real number, the result is always non-negative. The only way that each squared deviation score can be equal to 0 is if all of the scores equal the mean. Thus, when the standard deviation equals 0, all the scores are identical and equal to the mean.

#### Is a standard deviation of 0 good?

This means that every data value is equal to the mean. This result along with the one above allows us to say that the sample standard deviation of a data set is zero if and only if all of its values are identical.

**Why do z scores have a mean of 0?**

The mean of the z-scores is always 0. The standard deviation of the z-scores is always 1. The sum of the squared z-scores is always equal to the number of z-score values. Z-scores above 0 represent sample values above the mean, while z-scores below 0 represent sample values below the mean.

**Can a mean be zero?**

Mean is the average of the data that can be calculated by dividing the sum of the data by the numbers of the data. The mean of any normal distribution is not zero. However, we can normalize the data so that it has zero mean and one standard deviation, that is called as standard normal distribution.

## Can you average z score?

Of course you can average z scores — you simply add them and divide by the number of values, that’s an average of a set of z-scores.