Data files for Reyes & Bernido, submitted, 2023, A Model-Independent Determination of Red Noise in Pulsar Timing Arrivals. In this work, we analyze the pulsar timing data from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav; Arzoumanian et al 2018). For 23 pulsars with 820 MHz data, we show that an evaluation of the mean square deviation (MSD) and probability distribution (PDF) of timing residuals can provide a straightforward way of determining the presence of red noise. The model-free method presented could complement the normally more sophisticated model-dependent way of determining red noise in timing residuals. Data available here: - ts.zip - uniform time-series of timing residuals for the 23 pulsars - msd.zip - mean square deviation vs. lag time for the 23 pulsars - pdf.zip - probability distributions for lag times equal to 30, 150, 300, 900, and 1200 days for the 23 pulsars