Groups can make precise collective estimations in cases like the weight of an object or the number of items in a volume. However, in others tasks, for example those requiring memory or mental calculation, subjects often give estimations with large deviations from factual values. Allowing members of the group to communicate their estimations has the additional perverse effect of shifting individual estimations even closer to the biased collective estimation. Here we show that this negative effect of social interactions can be turned into a method to improve collective estimations. We first obtained a statistical model of how humans change their estimation when receiving the estimates made by other individuals. We confirmed using existing experimental data its prediction that individuals use the weighted geometric mean of private and social estimations. We then used this result and the fact that each individual uses a different value of the social weight to devise a method that extracts the subgroups resisting social influence. We found that these subgroups of individuals resisting social influence can make very large improvements in group estimations. This is in contrast to methods using the confidence that each individual declares, for which we find no improvement in group estimations. Also, our proposed method does not need to use historical data to weight individuals by performance. These results show the benefits of using the individual characteristics of the members in a group to better extract collective wisdom. 