Usage of "in contrast"

The use of in contrast isn’t quite right here, and it isn’t really clear what is meant. Do the two sentences mean that the statistics are complete, but that they show a result lower than might have been expected? If so, you need to say something like The figures are complete, but they show a disappointingly low result.

EDIT: I see now that you are asking whether in contrast can be used on its own to introduce an opposing sentence. It can. For example, I might say It rained the whole of May. In contrast, June was a very dry month.

It follows in principle that you can use it that way in your example, but it remains unclear what two items are being contrasted. That may because of the use of completeness (which is not a good choice here anyway). Does it mean that the statistics are complete, or that whatever it is they describe is complete?

The word "contrast" conveys a stark difference in the degree to which two otherwise similar objects possess an attribute. Dark, depressing books and bonobos are too dissimilar to be in contrast, whereas the former do contrast with light hearted, trivial books.

If there is a valid context for comparison between the statistics and the figure, and this comparison would indicate that they are at opposite ends of the same spectrum, then yes, using "in contrast" is appropriate.

To address your edit, I believe all of the following are correct:

• Contrastingly, the figure shows good completeness.
• In contrast to this, the figure shows good completeness.
• In contrast, the figure shows good completeness.

The last one is somewhat ambiguous, so I would avoid using it. Additionally, I have removed the "a", which is incorrect.

A better alternative would be:

The statistics illustrate a low overall result. The figure, on the contrary, shows a good completeness.

The free dictionary:

on the contrary
just the opposite, esp. of something said or believed The evidence of history, on the contrary, shows that these ancient people had a very advanced culture.

You could also state it in a much simpler way:

The statistics illustrate a low overall result. The figure, however, shows a good completeness.

It is not clear what you are contrasting. What is the "figure"? When you contrast things you need to specify what attribute it's about. You've tried to contrast the outcome in an unclear fashion. Only in common turn of phrase (e.g. dry vs. wet weather) can you leave off exactly what is being contrasted. You're comparing unlike things, making it confusing. Statistics is a field of study and the figure is some number. Maybe if you used tighter terminology it would become clearer what you are contrasting. There is a tendency by non-native English speakers (like myself) to use words like contrasting in the hope that it helps to show or strengthens the case in otherwise unclear phrases. It does not.