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Many real-world datasets are incomplete due to factors such as data collection failures or misalignments between fused datasets. Visualizations of incomplete datasets should allow analysts to draw conclusions from their data while effectively reasoning about the quality of the data and resulting conclusions. We conducted a pair of crowdsourced studies to measure how the methods used to impute and visualize missing data may influence analysts' perceptions of data quality and their confidence in their conclusions. Our experiments used different design choices for line graphs and bar charts to estimate averages and trends in incomplete time series datasets. Our results provide preliminary guidance for visualization designers to consider when working with incomplete data in different domains and scenarios.