Measure the fluctuation of data I have 2 series of data, for example:
s1: 0.3 0.3 0.4 0.8 0.6 0.5 0.7
s2: 0.7 0.7 0.6 0.8 0.7 0.5 0.6
It's easy to see that the data in s1 is fluctuating a lot (min=0.3, max=0.8) while in s2 all the values close to others.
Which metric should I use to measure the fluctuation like this? I tried with standard deviation but it's not very clear.
 A: Depending on what exactly you are trying to measure, there could be a selection of metrics to choose. Standard deviation is indeed a good choice to measure the amount of variation or dispersion of a dataset. 
The formula is typically given by:
$\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N} (x_i-\mu)^2 }$
where $N$ is the sample size, $x_i$ is each individual observation, and $\mu$ is the mean of the dataset.
Below I've plotted the two distributions, you can see that $\sigma_{s1}=0.2$ and $\sigma_{s2}=0.1$. This is telling you that on average, the data in s1 varies twice as much with respect to the mean value compared to s2. I encourage you to read up on the metric to gather a better understanding.
Edit:
As @NickCox has rightly pointed out, standard deviation is also commonly formulated as:
$\sigma = \sqrt{\frac{1}{N-1}\sum_{i=1}^{N} (x_i-\mu)^2 }$
Note that for relatively large sample sizes this will make little appreciable difference although please see this this answer for a discussion on the point.

A: Standard deviations are not scale invariant, i.e., they are expressed in the units of the measure. For a scale invariant metric that is dimensionless and comparable across measures that differ widely in location and scale, use the coefficient of variation. The CV is calculated as the std dev divided by the mean times 100.
A: I would suggest that you need to understand the underlying distribution of the data first before determining what measure of variability to use. So it's not a simple as saying it's "standard deviation". 
Certainly for Normal distributions, standard deviation is a good one. I personally use +/- 2 standard deviation for comparison if I do want to find a difference, or +/- 3 standard deviation for comparison if I don't want to find a difference.
Standard deviation as defined for Normal Distribution wouldn't work for Binomial Distribution (coin flipping e.g.). The standard deviation is based on the probability of either event happening.
Std Deviation as defined for Normal Distribution also doesn't work for Poisson Distribution (length of a queue e.g.), though using the central limit theorem, your distribution can approximate a Normal.
