Research in the field of low-temperature electronics is limited by the small number of electrical contacts available on cryogenic set ups. This not only restricts the number of devices that can be fabricated, but also the device and circuit complexity. We present an on-chip multiplexing technique which significantly increases the number of devices locally measurable on a single chip, without the modification of existing fabrication or experimental set-ups. We demonstrate the operation of the multiplexer by performing electrical measurements of 256 quantum wires formed by split-gate devices using only 19 electrical contacts on a cryogenic set-up. The multiplexer allows the measurement of many devices and enables us to perform statistical analyses of various electrical features which exist in quantum wires. We use this architecture to investigate spatial variations of electrical characteristics, and reproducibility on two separate cooldowns. These statistical analyses are necessary to study device yield and manufacturability, in order for such devices to form the building blocks for the realisation of quantum integrated circuits. The multiplexer provides a scalable architecture which makes a whole series of further investigations into more complex devices possible.