Difference between standard deviation and kurtosis

In summary, standard deviation and kurtosis may seem to measure the same thing, but they actually measure different aspects of a distribution. While standard deviation measures the spread of the data, kurtosis measures the width of the distribution in relation to a normal distribution. A higher standard deviation indicates a wider spread of data, while a lower kurtosis suggests a distribution with a sharper peak and longer tails compared to a normal distribution.
  • #1
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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.

I'm sure I'm wrong about this so can someone help me out with what I'm missing?
 
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  • #2
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
Ok i understand now. I think I was looking at figures incorrectly. Thank you.
 

FAQ: Difference between standard deviation and kurtosis

What is standard deviation?

Standard deviation is a measure of how spread out a set of data is from its mean or average. It tells us how much the data points deviate from the mean. The higher the standard deviation, the more spread out the data is.

What is kurtosis?

Kurtosis is a measure of the peakedness or flatness of a distribution. It tells us how much of the data is concentrated around the mean and how much is spread out towards the tails of the distribution. A high kurtosis means a distribution has a sharp peak and heavy tails, while a low kurtosis means a distribution is flatter and has lighter tails.

What is the difference between standard deviation and kurtosis?

The main difference between standard deviation and kurtosis is that they measure different aspects of a distribution. Standard deviation measures the spread or variability of the data, while kurtosis measures the shape or peakedness of the distribution. Standard deviation is affected by outliers, while kurtosis is not affected by outliers.

How are standard deviation and kurtosis related?

Standard deviation and kurtosis are both measures of the variability of a distribution, but they are not directly related. A distribution can have a high standard deviation and low kurtosis, or a low standard deviation and high kurtosis. However, a high standard deviation can result in a higher kurtosis, as more extreme values can contribute to a sharper peak and heavier tails in the distribution.

Which one is a better measure of variability: standard deviation or kurtosis?

Neither standard deviation nor kurtosis is a better measure of variability; they both provide different information about a distribution. Standard deviation is a more commonly used measure and is useful for comparing the spread of different distributions. Kurtosis, on the other hand, is useful for identifying the shape of a distribution and detecting outliers. The choice of which measure to use depends on the specific research question and the type of data being analyzed.

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