Chapter #2: Central Tendency
Measures of Central Tendency
Mayer’s intuition about the relation between the number of observations and accuracy eventually led to the theory of central tendency. In his case, he simply took the average of the observations to generate a new result which on average would retain the accuracies of the individual observations and cancel out the errors - assuming that the errors occurred at random.
Technically, Mayer’s central tendency was an average (or mean), computed by summing up all of the observations and dividing them by the total number of observations. For example, if we have 3 observations with the following values:
5 7 2
We will add them together and divide by 3 to generate the mean: (5 + 7 + 2) / 3 = 4.67
Other measures of central tendency exist besides the mean. If, for example, we want to know which observation occurs the most frequently in our dataset, we simply count the number of occurrences for each value:
1 4 2 4 3 3 4
Which in this case would be 4, since it occurs three times in this dataset - more than any of the other values.
One other widely used measure of central tendency is the median, which is the observation that stands midway between all of the values in the dataset. Just as a median divides a road, the median divides the dataset into two equal halves:
1 3 5 6 9
The value 5 in this dataset has two numbers that are lower than it, and two numbers that are higher.