Letxandrbe respectively the observed mean and range in a random sample of sizenfrom a normal population. Values ofk1are tabulated which ensure a probability β that the pair of limitsx±k1rwill include at least a proportionpof the population. For tolerance limits of the formx±k2r, wherexis the grand mean andrthe mean range inNsamples of sizemeach, necessary tables of the factork2are provided for situations wheremis either 4 or 5, these being common group sizes in control chart analysis.