This is the 81st most frequent Ukrainian word.
даними
"Даними" in English means "data."
In this sentence, 'даними' is instrumental plural and refers to 'data', used as an object of the preposition 'на основі' (on the basis of).
На основі зібраних даними, ми зробили висновки.
Based on the collected data, we made conclusions.
Here, 'даними' is instrumental plural and specifies 'data' as the tools or means required for an action.
Ці даними необхідно обчислити з великою точністю.
These data need to be calculated with great accuracy.
In this case, 'даними' is instrumental plural used to specify 'data' as the items being provided.