# Thread: Measure Volatility or Stability Of Lists of Floating Point Numbers

1. ## Measure Volatility or Stability Of Lists of Floating Point Numbers

Hi,
Wonder if anyone can help.

I have a set of lists of numbers, around 300 lists in the set, each list of around 200 numbers. What I wish to calculate is the "relative stability" of each list.

For example:

List A: 100,101,103,99,98 - the range is v small - so stable.
List B: 0.3, 0.1, -0.2, 0.1 - again, v small range, so stable.
List C: 0.00003, 0.00002, 0.00007, 0.00008 - stable.

Now, I could use standard deviation - but the values returned by the standard deviation will be relative to the values within each list. So std for list C would be tiny in comparison to std for list A - and therefore numerically not give me a comparable measure of stability/volatility enabling me to meaningfully ask: if list A more or less stable than list C?

So, I wondered if anyone had any suggestions for a measure that will be comparable across such lists?

Many thanks for any help.
R

2. ## Re: Measure Volatility or Stability Of Lists of Floating Point Numbers

Lists A and C are relatively stable, in that the SD is small compared with the mean. For these you can use the relative SD or coefficient of variation = CV = SD/mean, often expressed as a percentage. These are typical of laboratory measurements. The relative accuracy stays the same if you change the units.
List B is something different. As you have noted, its absolute range is small compared with that of list A but large compared with that of list C and it is very large compared to its mean. Its CV is potentially very large. List B is typical of measurement errors or laboratory measurements that are below the lower threshold of the device.
I think you will have difficulty getting a scheme which will be able to compare all three lists. kat

3. ## Re: Measure Volatility or Stability Of Lists of Floating Point Numbers

Hi katxt,

Thanks v much for replying. The variation coefficient, sd/mean, is almost certainly what I want. I appreciate it's not a fit for all cases. Thanks v much.

R

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