The need for data compression, a consequence of the demands made on the telemetry system of a space vehicle, prompts consideration of the use of sample quantiles in estimating population parameters and obtaining tests of goodness of fit for large samples. In this paper optimal unbiased estimators of the mean and standard deviation are given using up to twenty quantiles when the parent population is normal. Moreover, the estimators are relatively insensitive to deviations from normality. A distribution-free goodness-of-fit test is presented based on the sum of the squares of four quantiles after an orthogonal transformation to independent normal deviates. If a frequency function is of the formf(x; p) =pf1(x) + (1 -p)f2(x), 0 <p< 1, wheref1andf2are normal frequency functions, the distribution is likely to be bimodal. Another goodness-of-fit test is obtained using four quantiles, which is likely to have considerable power with a null hypothesis of normality and the alternative hypothesis of bimodality. The “data compression ratios” obtained with the use of a quantile system can be on the order of 100 to 1.