This article presents the data from two surveys that asked about everyday encounters with artificial intelligence (AI) systems that are perceived to have attributes of mind. In response to specific attribute prompts about an AI, the participants qualitatively described a personally-known encounter with an AI. In survey 1 the prompts asked about an AI planning, having memory, controlling resources, or doing something surprising. In survey 2 the prompts asked about an AI experiencing emotion, expressing desires or beliefs, having human-like physical features, or being mistaken for a human. The original responses were culled based on the ratings of multiple coders to eliminate responses that did not adhere to the prompts. This article includes the qualitative responses, coded categories of those qualitative responses, quantitative measures of mind perception and demographics. For interpretation of this data related to people's emotions, see Feeling our Way to Machine Minds: People's Emotions when Perceiving Mind in Artificial Intelligence Shank et al., 2019.