Data becomes information when it becomes relevant to your decision problem. Information becomes fact when the data can support it.
Fact becomes knowledge when it is useful in forming a human decision.
Statistics arose from the need to place knowledge on a systematic evidence base. This required a study of the laws of probability, the development of measures of data properties and relationships, and so on. Wisdom is about knowing how something technical can be best used to meet the needs of the decision-maker, without disguising or misrepresenting the truth.