Previously we have used Singular Spectrum Analysis (SSA) to deconstruct the global-mean near-surface temperature observations of the Hadley Centre—Climate Research Unit that extend from 1850 through 2012. While SSA is a very powerful tool, it is rather like a statistical “black box” that gives little intuition about its results. Accordingly, here we use the simplest statistical tool to provide such intuition, the Simple Moving Average (SMA). Firstly we use a 21-year SMA. This reveals a nonlinear trend and an oscillation of about 60 years' length. Secondly we use a 61-year SMA on the raw observations. This yields a nonlinear trend. We subtract this trend from the raw observations and apply a 21-year SMA. This yields a Quasi-periodic Oscillation (QPO) with a period and amplitude of about 62.4 years and 0.11°C. This is the QPO we discovered in our 1994 Nature paper, which has come to be called the Atlantic Multidecadal Oscillation. We then subtract QPO-1 from the detrended observations and apply an 11-year SMA. This yields QPO-2 with a period and amplitude of about 21.0 years and 0.04°C. We subtract QPO-2 from the detrended observations minus QPO-1 and apply a 3-year SMA. This yields QPO-3 with a period and amplitude of about 9.1 years and 0.03°C. QPOs 1, 2 and 3 are sufficiently regular in period and amplitude that we fit them by sine waves, thereby yielding the above periods and amplitudes. We then subtract QPO-3 from the detrended observations minus QPOs 1 and 2. The result is too irregular in period and amplitude to be fit by a sine wave. Accordingly we represent this unpredictable part of the temperature observations by a Gaussian probability distribution (GPD) with a mean of zero and standard deviation of 0.08°C. The sum of QPOs 1, 2 and 3 plus the GPD can be used to project the natural variability of the global-mean near-surface temperature to add to, and be compared with, the continuing temperature trend caused predominantly by humanity’s continuing combustion of fossil fuels.