For statistical data on a population, a percentile represents the percentage of the total data that falls below a given data point. Consider the results of a state-wide standardized test; a graph of the scores from least to greatest might take the following shape.

If a student named Jane scored $80\%$ on this test, her score was better than $96\%$ of the other scores recorded in the state. Therefore, Jane's score was at the $96^{\text{th}}$ percentile of the test scores. Compare some other test scores with the rest of the data using the graph below.

Normally distributed data is commonly divided into bands, or subsections, that have the width of one standard deviation $\sigma.$

Given that half the population is to the left of the median $\mu,$ and the first band to the right of the median contains $34.1\%$ of the population, it can be stated that the $84$th percentile for normally distributed data is $\mu + \sigma.$