Voting technique for determining the most representative average of numerical data sets

This study introduces a voting technique to determine the Most Representative Average (MRA) of a numeric data set and addresses the existing limitation of mode’s potential non-existence and lack of uniqueness often encountered in data analysis. The technique requires every data point to cast a vote for the average it is closest to, treating all observations and averages with equal weights. The average with the highest number of votes is the MRA. This not only offers a participatory and proximity-based alternative to traditional measures of central tendency but also addresses mode’s limitation. Unlike the arithmetic mean, which minimizes total distance, or the median, which reflects positional center, the MRA reflects the collective closeness preferences of the data points. The study uses the mean SAT scores from each state of the United States over a six-year period, comprising 18 educational datasets with varying characteristics, to illustrate the technique. The findings indicate that the MRA is not solely dependent on the mode, but other alternatives can also be viable contenders based on the data characteristics. Ties are rare and this points to the effectiveness and reliability of the technique in real-world data. Therefore, the study advocates the use of the voting technique for its fairness, adaptability, and ability as a complementary tool for identifying a context-sensitive representative statistic. Future work should investigate the statistical properties of MRA and its extension to high-dimensional and weighted data.