The mode is considered a single value that occurs more often than any other in a
set of data. It is not the frequency of the most numerous number, but the value of the
number itself. Often there is more than one mode if two or more values are commonly
found in the set—often called a multi-modal population.
What is the rangeof a set of numbers?
The range of a sample (or data set) is used to characterize the spread or dispersion
among observations in a given population, as it is the distance between the highest and
lowest numbers. In statistics, it is often (logically) referred to as the statistical range.
Numerically, it is represented by the highest score minus the lowest score. For exam-
ple, for the range of the numbers 34, 84, 48, 65, 92, and 22, the range is 92 22 70.
What is the average deviation?
The average deviation is a way of characterizing the spread (dispersion) among the
measures in a given population. To determine the average deviation, compute the
mean, then specify the distance between each score and that mean without regard to
whether the score is above or below the mean. The following is the notation for this
calculation (the symbol stands for “sum of”; the symbol | | stands for absolute value):
in which xis the various values of the samples, is the mean (or average) for the
entire population, and Nis the number of samples (the two vertical lines representing
the absolute value means there are no negative numbers on top).
For example, if we have six people who weighed 166, 134, 189, 141, 178, and 150,
the equation would read (is the average, or the total weight divided by the number
of people, or 958/6 159.67; n6, or the number of people; and xare the individual
weights of the people):
The average deviation for this example is 18.
What is the variance?
The variance is the average of the squares of a set’s deviations. It is used to charac-
terize the spread among the measures of a given population. First, calculate the
mean of the scores; then measure the amount that each score deviates from the
mean. Finally, square that deviation (in other words, multiply it by itself, add all of
them together, then divide by the total number of scores). An even easier way is to
.. ..
6
R 166 -+-++-159 67 134 159 67 g 178 159 67 + 150 - 159 67
N
x-nR
260
