This study aims to explore Bayesian multilevel modeling to investigate variations of average academic achievement of grade eight school students. A sample of 636 students is randomly selected from 26 private and government schools by a two-stage stratified sampling design. Bayesian method is used to estimate the fixed and random effects. Input and process quality indicators of education such as student to class ratio, student to teacher ratio, availability of teaching learning resources at school, teaching methods, and standard of course curriculum are found to be significantly affecting the academic achievement of the students. The effects of student level covariates: absence from class, academic motivation, academic self concept, study time, family income, mother's education, parents' employment status, work demand at home, and parent's follow-up of child are significantly varying from school to school. The results show that a large proportion of academic achievement variation is accounted to between schools. It is interesting to found out that the within school variation is very high for government schools while the between school variation is very high for private schools. There is uniformity across the government schools with high individual differences among students. However, there is lesser uniformity across the private schools with lesser individual differences of students. The findings in this study indicate that private schools are in a better position in maintaining quality of education at grade eight. Efficient academic management is needed at the government schools that can improve quality of education at the level.