Ellenberg (2014) noted that when you use sample data to rank states by brain cancer rates, the highest ranking state (South Dakota) and the nearly lowest ranking state (North Dakota) had relatively small sample sizes.
Also, when schools in North Carolina were ranked by their average improvement in test scores, the best and the worst schools were schools with very small sample sizes. Explain how these results could merely reflect sample means and proportions having larger variabilitywhensample sizes are smaller. (Hint:What would you expect with the sample if all the population means were identical?)