The Quick Count and Election Observation

THE QUICK COUNT AND ELECTION OBSERVATION
8 and 10, the number in the middle of the observations is 7; there are three
observations smaller than 7 and three observations with values that are greater
than 7. The mode for this dataset, however, is 8 because 8 occurs most frequently.
The arithmetic mean for this data set is 6.14. Statisticians usually
report the mean, rather than the median or the mode, as the most useful measure
of central tendency.
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Measures of Dispersion
A second feature of data concerns measures of dispersion, which indicate how
widely, or how narrowly, observed values are distributed. From the example above,
it is clear that any given data set will have an arithmetic mean. However, that mean
provides no information about how widely, or narrowly, the observed values are
dispersed. The following data sets have the same arithmetic mean of 3:
2, 2, 3, 4, 4
-99, -99, 3, 99, 99,
These two datasets have quite different distributions. One way to express the
difference in the two datasets is to consider the range of numbers. In the first
set, the smallest number is 2 and the largest number is 4. The resulting range,
then, is 4 minus 2, or 2. In the second set, the smallest number is negative 99
and the largest number is positive 99. The resulting range is positive 99 minus
negative 99, or 198.
Obviously, the different ranges of the two datasets capture one aspect of the
fundamental differences between these two sets of numbers. Even so, the range
is only interested in two numbers -- the largest and the smallest; it ignores all
other data points. Much more information about the spread of the observations
within the dataset can be expressed with a different measure, the variance.
In non-technical terms, the variance expresses the average of all the distances
between each observation value and the mean of all observation values. The
variance takes into account the arithmetic mean of a dataset and the number
of observations, in addition to each of the datapoints themselves. As a result,
it includes all the information needed to explain the spread of a dataset. The
variance for any set of observations can be determined in four steps:
1. Calculate the arithmetic mean of the dataset.
2. Calculate the distance between every data point and the mean, and
square the distance.
3. Add all the squared distances together.
4. Divide this by the number of observations.