Cerebellar Ataxia (CA) leads to deficiencies in muscle movement and lack of coordination that is often manifested as gait and balance disabilities. Conventional CA clinical assessments are subjective, cumbersome and provide less insight into the functional capabilities of patients. This cross-sectional study investigates the use of wearable inertial sensors strategically positioned on the front-chest and upper-back locations during the Romberg and Trunk tests for objective assessment of human postural balance due to CA. The primary aim of this paper is to quantify the performance of postural stability of 34 patients diagnosed with CA and 22 healthy subjects as controls. Several forms of entropy descriptions were considered to uncover characteristics of movements intrinsic to CA. Indeed, correlation with clinical observation is vital in ascertaining the validity of the inertial measurements in addition to capturing unique features of movements not typically observed by the practicing clinician. Both of these aspects form an integral part of the underlying objective assessment scheme. Uncertainty in the velocity contained a significant level of information with respect to truncal instability and, based on an extensive clustering and discrimination analysis, fuzzy entropy was identified as an effective measure in characterising the underlying disability. Front-chest measurements demonstrated a strong correlation with clinical assessments while the upper-back measurements performed better in classifying the two cohorts, inferring that the standard clinical assessments are relatively influenced by the frontal observations. The Romberg test was confirmed to be an effective test of neurological diagnosis as well as a potential candidate for objective assessment resulting in a significant correlation with the clinical assessments. In contrast, the Trunk test is observed to be relatively less informative.