Measures of Central Tendency

Author(s)

Prerequisites

1. Compute mean
2. Compute median
3. 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.

Arithmetic Mean

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.

Median

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 50th percentile.

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.

Mode

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 frequency distribution.

feedback