Many model-based methods have been developed over the last several decades for analysis of electroencephalograms (EEGs) in order to understand electrical neural data. In this work, we propose to use the functional boxplot (FBP) to analyze log periodograms of EEG time series data in the spectral domain. The functional bloxplot approach produces a median curve—which is not equivalent to connecting medians obtained from frequency-specific boxplots. In addition, this approach identifies a functional median, summarizes variability, and detects potential outliers. By extending FBPs analysis from one-dimensional curves to surfaces, surface boxplots are also used to explore the variation of the spectral power for the alpha (8–12 Hz) and beta (16–32 Hz) frequency bands across the brain cortical surface. By using rank-based nonparametric tests, we also investigate the stationarity of EEG traces across an exam acquired during resting-state by comparing the spectrum during the early vs. late phases of a single resting-state EEG exam.