Approximation of Sample Mean and Standard Deviation from Percentiles and Application to Reference Model for Sprint Time of Elite Soccer Players

The original goal of this project was to conduct meta-analysis and develop a reference model for 20-meter sprint time of elite soccer players with respect to age group. According to the likelihood function, we found that age-specific sample means and standard deviations are sufficient statistics. However, instead of the two sufficient statistics, the sample 10-th percentile, 90th-percentile, and quartiles were given to us. To deal with this unexpected challenge, we studied and compared methods of approximating the sample mean and standard deviation given various combinations of percentiles. Simulation studies showed that the likelihood method presented in this paper is superior when the sample 10-th percentile, 90-th percentile, and quartiles are given, and we applied the likelihood method to the meta-analysis and developed the reference model for 20-meter sprint time.