A computer-implemented method, comprising: at a distributed computer system including multiple computers, each computer having one or more processors and memory storing multiple event records, each event record including a predefined time interval: receiving a query from a client, wherein the query includes predefined criteria that specify a predefined time period and a predefined accuracy threshold; dynamically selecting one or more computers based on having at least a predefined number of candidate event records on the selected computers that might satisfy the predefined criteria and by applying at least one of the predefined criteria including the predefined accuracy threshold to a predefined sharding function, wherein dynamically selecting the one or more computers includes: choosing at least two computers that have replicas of a same set of event records and selecting one of the at least two computers that has a relatively lower workload for processing the query; at each of the selected computers: identifying a number of candidate event records stored in the memory of the computer; and determining, among the identified candidate event records, a count of qualified event records that satisfy the predefined criteria, wherein each qualified event record has a predefined time interval that at least partially overlaps the predefined time period associated with the query; aggregating the respective counts of qualified event records determined by the selected computers; statistically projecting the aggregated count of qualified event records into an estimated total count of qualified event records on the distributed computer system, wherein the estimated total count of qualified event records has an associated confidence level; and returning a query result to the requesting client, wherein the query result is a partial query result having an accuracy that is above the predefined threshold and includes the estimated total count of qualified event records and its associated confidence level. receiving a query from a client, wherein the query includes predefined criteria that specify a predefined time period and a predefined accuracy threshold; dynamically selecting one or more computers based on having at least a predefined number of candidate event records on the selected computers that might satisfy the predefined criteria and by applying at least one of the predefined criteria including the predefined accuracy threshold to a predefined sharding function, wherein dynamically selecting the one or more computers includes: choosing at least two computers that have replicas of a same set of event records and selecting one of the at least two computers that has a relatively lower workload for processing the query; at each of the selected computers: identifying a number of candidate event records stored in the memory of the computer; and determining, among the identified candidate event records, a count of qualified event records that satisfy the predefined criteria, wherein each qualified event record has a predefined time interval that at least partially overlaps the predefined time period associated with the query; identifying a number of candidate event records stored in the memory of the computer; and determining, among the identified candidate event records, a count of qualified event records that satisfy the predefined criteria, wherein each qualified event record has a predefined time interval that at least partially overlaps the predefined time period associated with the query; aggregating the respective counts of qualified event records determined by the selected computers; statistically projecting the aggregated count of qualified event records into an estimated total count of qualified event records on the distributed computer system, wherein the estimated total count of qualified event records has an associated confidence level; and returning a query result to the requesting client, wherein the query result is a partial query result having an accuracy that is above the predefined threshold and includes the estimated total count of qualified event records and its associated confidence level.