We study how choice architecture that companies deploy during data collection influences consumers' privacy valuations. Further, we explore how this influence affects the quality of data collected, including both volume and representativeness. To this end, we run a large-scale choice experiment to elicit consumers' valuation for their Facebook data while randomizing two common choice frames: default and price anchor. An opt-out default decreases valuations by 14-22% compared to opt-in, while a $0-50 price anchor decreases valuations by 37-53% compared to a $50-100 anchor. Moreover, in some consumer segments, the susceptibility to frame influence negatively correlates with consumers' average valuation. We find that conventional frame optimization practices that maximize the volume of data collected can have opposite effects on its representativeness. A bias-exacerbating effect emerges when consumers' privacy valuations and frame effects are negatively correlated. On the other hand, a volume-maximizing frame may also mitigate the bias by getting a high percentage of consumers into the sample data, thereby improving its coverage. We demonstrate the magnitude of the volume-bias trade-off in our data and argue that it should be a decision-making factor in choice architecture design.