As smart grids are getting popular and being widely implemented, preserving the privacy of consumers is becoming more substantial. Power generation and pricing in smart grids depends on the continuously gathered information from the consumers. However, having access to the data relevant to the electricity consumption of each individual consumer is in conflict with its privacy. One common approach for preserving privacy is to aggregate data of different consumers and to use their smart-meters for calculating the bills. But in this approach, malicious consumers who send erroneous data to take advantage or disrupt smart grid cannot be identified. In this paper, we propose a new statistical-based scheme for data gathering and billing in which the privacy of consumers is preserved, and at the same time, if any consumer with erroneous data can be detected. Our simulation results verify these matters.