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Privacy concerns can be a major barrier to collecting aggregate data from the public. Recent research proposes negative surveys that collect negative data, which is complementary to the true data. This opens a new direction for privacy-aware data collection. However, the existing approach cannot avoid certain errors when applied to many spatial data collection tasks. The errors can make the data unusable in many real scenarios. We propose Gaussian negative surveys. We modulate data collection based on Gaussian distribution. The collected data can be used to compute accurate spatial distribution of participants and can be used to accurately answer range aggregate queries. Our approach avoids the errors that can occur with the existing approach. Our experiments show that we achieve an excellent balance between privacy and accuracy.