This paper develops a mathematical theory to analyze and interpret DNA polymorphism data obtained through DNA sequencing or restriction enzyme techniques. The theory assumes that evolutionary changes in nucleons are solely due to mutation and random genetic drift. The statistical properties of the number of nucleotide differences and heterozygosity are investigated, revealing that estimates of these quantities have significant variance, much of which is due to stochastic factors. Increasing sample size does not significantly reduce this variance. The distribution of sample allele frequencies is also studied, showing that a small number of samples are sufficient to understand the distribution pattern. The paper discusses the evolutionary relationship among nucleons sampled from a single or two populations, considering the topological relationships and branch lengths. It provides formulas for the probability distribution of the number of nucleotide differences between randomly chosen nucleons, the mean and variance of these differences, and the expected nucleon diversity. The results indicate that the average number of nucleotide differences is more informative than heterozygosity or nucleon diversity in measuring genetic variation within populations, despite its large variance. The paper also explores the distribution of sample nucleomorph frequencies, showing that a small sample size is often sufficient to understand the distribution unless the population size is very large. Finally, it discusses the implications of these findings for interpreting data on DNA polymorphism, particularly in the context of evolutionary trees constructed from mitochondrial DNA sequences.This paper develops a mathematical theory to analyze and interpret DNA polymorphism data obtained through DNA sequencing or restriction enzyme techniques. The theory assumes that evolutionary changes in nucleons are solely due to mutation and random genetic drift. The statistical properties of the number of nucleotide differences and heterozygosity are investigated, revealing that estimates of these quantities have significant variance, much of which is due to stochastic factors. Increasing sample size does not significantly reduce this variance. The distribution of sample allele frequencies is also studied, showing that a small number of samples are sufficient to understand the distribution pattern. The paper discusses the evolutionary relationship among nucleons sampled from a single or two populations, considering the topological relationships and branch lengths. It provides formulas for the probability distribution of the number of nucleotide differences between randomly chosen nucleons, the mean and variance of these differences, and the expected nucleon diversity. The results indicate that the average number of nucleotide differences is more informative than heterozygosity or nucleon diversity in measuring genetic variation within populations, despite its large variance. The paper also explores the distribution of sample nucleomorph frequencies, showing that a small sample size is often sufficient to understand the distribution unless the population size is very large. Finally, it discusses the implications of these findings for interpreting data on DNA polymorphism, particularly in the context of evolutionary trees constructed from mitochondrial DNA sequences.