The arithmetic mean (often simply the mean) adds up the values of a numercal feature ina dataset, for example, the hights of people ina. room, and divides by the total number of indviduals. For example, the mean of the numbers [1,7,6,2,4] is (1+7+6+2+4)/5 = 20/5 = 4. The term average may refer to the arithmetic mean or may refer to the median. The median is often a better centrality measure than the mean as it is more stable espedcially given extreme values, or for non-Normal distributions such as the power law distributions. However, the mean has nice mathematical properties that make it easier to process, for example, if you have caclualted the mean of two datasets (say m1 and m2) and know how many in each (say N1 and N2) it is possible to combine these:
overall mean = (m1 x N1 + m2 x N2) / (N1 + N2)
Used on pages 137, 203