In this article, representativity between two multidimensional acoustical spaces of vowel has been formulated based on the geometric mean of correlation of average directional vector, variance-covariance matrices, and Mahalanobis distance. Generally, the multidimensional spaces formed by different combinations of acoustical features of vowel are considered as the vowel perceptual spaces. Therefore, ten bangla vowel-sounds (/অ/ [/a/], /আ/ [/ã/], / ই/ [/i/] , /ঈ/ [/ĩ/], /উ/ [/u/], / ঊ/ /ũ/, /এ/ [/e/], /ঐ/ [/ai/] , /ও/ [/o/] and /ঔ/ [/au/]) are collected from each native Bengali speaker to build the perceptual space of the speaker using the acoustical features of vowels. Similarly, total nine perceptual spaces are constructed from nine speakers and these are utilized to evaluate representativity. Using the proposed method, representativities of differently constructed perceptual spaces have been evaluated and compared numerically. Furthermore, dominating and representative acoustical features are also identified from the principal components of the perceptual spaces.