Can standard deviation be greater than mean for positive numbers?

Can standard deviation be greater than mean for positive numbers?

Yes, SD can come out greater than the mean, when you have extreme variables or a mix of negative and positive values.

Does a higher standard deviation mean a higher mean?

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Can standard deviation be greater than range?

If you use the second formula, then it is pretty obvious that the standard deviation cannot exceed the range. The mean of the data has to be inside the range of the data, so no single term (before being squared) in the sum can exceed the range. You can achieve the maximum standard deviation for a very simple case.

Is standard deviation greater than mean deviation?

Standard deviation is always greater than mean deviation.

Why is standard deviation important in statistics?

Standard deviations are important here because the shape of a normal curve is determined by its mean and standard deviation. The standard deviation tells you how skinny or wide the curve will be. If you know these two numbers, you know everything you need to know about the shape of your curve.

What is the intuition behind the standard deviation?

Intuition behind standard deviation. From what I understand it is representative of the average of the differences of a set of observations in a data set from the mean of that data set. However it is NOT actually equal to the averages of the differences as it gives more weight to observations further from the mean.

Can a standard deviation be greater than the 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.

Is the utility of the standard deviation dependent on the law of errors?

As an aside: Note that the utility of the standard deviation is dependent on the applicability of the “law of errors”, also known as the “normal curve”, which arises from “a great many independent causes of error” (Airy 1875 pg 7). There is no reason to expect that deviations from a group mean of each individual should follow this law.

Why is standard deviation called error of mean square?

The standard deviation is called “error of mean square”. It is also discussed pages 20-21 and he justifies its use on page 48, showing that it is easiest to calculate by hand because there is no need for separate calculation of negative and positive errors. The term standard deviation was introduced by Pearson in the paper cited above on page 75.