Over the last century, the adoption of novel scientific methods for conducting the U.S. census has been met with wide-ranging receptions. Some methods were quietly embraced, while others sparked decades-long controversies. What accounts for these differences? We argue that controversies emerge from $\textit{arrangements of statistical imaginaries}$, putting into tension divergent visions of the census. To analyze these dynamics, we compare reactions to two methods designed to improve data accuracy (imputation and adjustment) and two methods designed to protect confidentiality (swapping and differential privacy), offering insight into how each method reconfigures stakeholder orientations and rhetorical claims. These cases allow us to reflect on how technocratic efforts to improve accuracy and confidentiality can strengthen -- or erode -- trust in data. Our analysis shows how the credibility of the Census Bureau and its data stem not just from empirical evaluations of quantification, but also from how statistical imaginaries are contested and stabilized.

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