# Difference between standard deviation and kurtosis

1. Jun 29, 2009

### blerg

I'm new to studying statistics but it seems to me like standard deviation and kurtosis measure the same thing.
The higher the standard deviation, the more spread out the data is, while the lower the kurtosis the more spread out the data is.

2. Jun 29, 2009

### D H

Staff Emeritus
Kurtosis measures something quite distinct from the variance. The kurtosis is the fourth moment about the mean divided by the square of the variance, less three. (Not everyone subtracts 3 from the result). Regardless of the variance, all normal distributions have a kurtosis of 0 (or 3 depending on how you define kurtosis).

One way to look at kurtosis is that it measures the width of a random distribution compared to that of a normal distribution with the same mean and variance as the distribution in question. If the distribution is symmetric about the mean, a distribution with a positive kurtosis will have a sharper peak and much longer tails than does the normal distribution. The opposite is the case for distributions with a negative kurtosis.

3. Jul 1, 2009

### blerg

Ok i understand now. I think I was looking at figures incorrectly. Thank you.