Measures of Central Tendency
- Compute mean
- Compute median
- Compute mode
This section gives only the basic definitions
of the mean , median and mode. A further discussion of the relative
merits and proper applications of these statistics is presented
in a later section.
The arithmetic mean is the most common measure
of central tendency. It simply the sum of the numbers divided
by the number of numbers. The symbol "μ"
is used for the mean of a population. The symbol "M" is used for
the mean of a sample. The formula for μ
is shown below:
μ = ΣX/N
where ΣX is the sum of all the numbers
in the population and
N is the number of numbers in the population.
The formula for M is essentially identical:
M = ΣX/N
where ΣX is the sum of all the numbers in the sample and
N is the number of numbers in the sample.
Although the arithmetic mean is not the only "mean"
(there is also a geometric mean), it is by far the most commonly
used. Therefore, if the term "mean" is used without
specifying whether it is the arithmetic mean, the geometric mean,
or some other mean, it is assumed to refer to the arithmetic mean.
This median is also
a frequently used measure of central tendency. The median is the
midpoint of a distribution: the same number of scores are above
the median as below it. For the data in Table 1, there are 31
scores. The 16th highest score (which equals 20) is the median
because there are 15 scores below the 16th score and 15 scores
above the 16th score. The median can also be thought of as the
Computation of the Median
When there is an odd number of numbers, the median
is simply the middle number. For example, the median of 2, 4,
and 7 is 4. When there is an even number of numbers, the median
is the mean of the two middle numbers. Thus, the median of the
numbers 2, 4, 7, 12 is (4+7)/2 = 5.5.
The mode is the most frequently occurring value.
With continuous, data such as response time measured to many decimals,
the frequency of each value is one since no two scores will be
exactly the same (see discussion of continuous
variables). Therefore the mode of continuous data is normally
computed from a grouped