SignificanceDigital technologies deeply impact the way that people interact. Therefore, it is crucial to understand how social influence affects individual and collective decision-making. We performed experiments where subjects had to answer questions and then revise their opinion after knowing the average opinion of some previous participants. Moreover, unbeknownst to the subjects, we added a controlled number of virtual participants always giving the true answer, thus precisely controlling social information. Our experiments and data-driven model show how social influence can help a group of individuals collectively improve its performance and accuracy in estimation tasks depending on the quality and quantity of information provided. Our model also shows how giving slightly incorrect information could drive the group to a better performance.