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This paper describes the theory and design of an advanced engineering prototype of a quantile system of data compression for space telemetry. The basic idea is to transmit a few quantiles (or percentage points, as they are sometimes called) of a histogram of experimental values formed aboard a spacecraft. Only these quantiles are transmitted to Earth, and yet a large part of the information that was contained in the original histogram can be reconstructed on Earth. Compression ratios on the order of 100 to 1 are obtainable at 100 percent efficiency (in the sense of variances of estimates) with a simple device that performs no on-board arithmetic operations. After summarizing the theoretical background governing the use of quantiles, we then consider what the design considerations of such a system should be. Data compression ratios are computed for a typical application of the quantile system. The detail description of the advanced engineering quantile system that has been built at the Jet Propulsion Laboratory is discussed; in addition, a block diagram is given and analyzed. An important feature of the quantile system is its self-adaptive feature. Examples are given whereby quantile systems for compressing telemetry data can find application in non-military and non-space technology. Finally, experimental results using the constructed system are given.