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In this module, we explore measurement and the various levels at which we can use measurement to describe individual observations. An observation in this context is known as a datum. An example of a datum could be how many conversations a person initiates in each day, or how many minutes per day a person spends watching television. Multiple observations of a characteristic in a population or in a sample are referred to as data. After we collect a set of data, we are usually interested in making some statistical summary statements about this large and complex set of individual values for a variable. With this data, we want to describe a collective such as a sample or a population in its entirety. This description is the first step in bridging the gap between the “measurement world” of our limited number of observations, and “real world” complexities We refer to this process as describing the distribution of a variable (Kachigan, 1986, p. 100).

Descriptive statistics do exactly that. They represent or epitomize some facet of a distribution. These descriptive statistics allow us to go beyond the mere description of a distribution. They can also be used for statistical inference, which permits generalizing from the limited number of observations in a sample to the entire population. But that is for a later discussion in this course. Descriptive statistics can be divided into two major categories: measures of central tendency and measures of dispersion or variability. Both kinds of measures focus on different essential characteristics of distributions. The measures of central tendency describe a distribution in terms of its most “frequent,” “typical,” or “average” data value. The information provided by these measures is not enough to convey all we need to know about a distribution. We need additional information about the distributions. This information is provided by a series of measures that are referred to as measures of dispersion.

There are several reasons why it is useful to consider the descriptions of central tendency and dispersion together. For the discussions, describe three reasons why it is useful to consider these measures together in the business world. Provide examples. We will discuss this in class.

Reference

Kachigan, S.K. (1986). Statistical analysis: An interdisciplinary introduction to univariate and multivariate methods. New York: Radius Press. (Chapter 4, “Central Tendency”; Chapter 5, “Variation”)