Abstract The daily volume of Tweets in Twitter is around 500 million, and the impact of this data on applications ranging from public safety, opinion mining, news broadcast, etc., is increasing day by day. Analyzing large volumes of Tweets for various applications would require techniques that scale well with the number of Tweets. In this work we come up with a theoretical formulation for sampling Twitter data. We introduce novel statistical metrics to quantify the statistical representativeness of the Tweet sample, and derive sufficient conditions on the number of samples needed for obtaining highly representative Tweet samples. These new statistical metrics quantify the representativeness or goodness of the sample in terms of frequent keyword identification and in terms of restoring public sentiments associated with these keywords. We use uniform random sampling with replacement as our algorithm, and sampling could serve as a first step before using other sophisticated summarization methods to generate summaries for human use. We show that experiments conducted on real Twitter data agree with our bounds. In these experiments, we also compare different kinds of random sampling algorithms. Our bounds are attractive since they do not depend on the total number of Tweets in the universe. Although our ideas and techniques are specific to Twitter, they could find applications in other areas as well.