Is it 40% or 0.4%? A variable, which should contain percents, also contains some "ratio" values, for example:
0.61
41
54
.4
.39
20
52
0.7
12
70
82

The real distribution parameters are unknown but I guess it is unimodal with most (say over 70% of) values occurring between 50% and 80%, but it is also possible to see very low values (e.g., 0.1%). 
Is there any formal or systematic approaches to determine the likely format in which each value is recorded (i.e., ratio or percent), assuming no other variables are available?
 A: Assuming 


*

*The only data you have is the percents/ratios (no other related explanatory variables)

*Your percents comes from a unimodal distribution $P$ and the ratios come from the same unimodal distribution $P$, but squished by $100$ (call it $P_{100}$).

*The percent/ratios are all between $0$ and $100$.


Then there's a single cutoff point $K$ (with $K < 1.0$ obviously) where everything under $K$ is more likely to be sampled from $P_{100}$ and everything over $K$ is more likely to be sampled from $P$.
You should be able to set up a maximum likelihood function with a binary parameter on each datapoint, plus any parameters of your chosen P.
Afterwards, find $K :=$ where $P$ and $P_{100}$ intersect and you can use that to clean your data.
In practice, just split your data 0-1 and 1-100, fit and plot both histograms and fiddle around with what you think $K$ is.
A: Here's one method of determining whether your data are percents or proportions: if there are out-of-bounds values for a proportion (e.g. 52, 70, 82, 41, 54, to name a few) then they must be percents. 
Therefore, your data must be percents. You're welcome. 
