In Wireless Sensor Networks (WSNs), the sensor nodes sense the same kind of data and forward it to the sink node. This redundant information sustains the reliability; but at the same time, sink node wastes its energy in processing the redundant data. So there is a need to eliminate the redundancy in sensed data up to adequate level in order to maintain the tradeoff between energy conservation and reliability. Data Gathering is a crucial technique in Wireless Sensor Networks (WSNs). Data gathering trees capable of performing aggregation operations are also referred to as Data Aggregation Trees (DATs). Most of the current literatures investigate the construction problem under Deterministic Network Model (DNM), whereas this paper is suitable for Probabilistic Network Model (PNM) due to any lossy links in WSN’s. Moreover, the load-balance factor is neglected when constructing DATs in current literatures.