Chapter 3 Measures of Central Tendency
3.7 Central Tendency and the Levels of Measurement
This chapter introduced a lot of new concepts and terminology so a recap is in order. The three measures of central tendency — the mode, the median, and the mean — provide information about the so-called “centre of gravity” of a variable’s distribution, or where the cases tend to cluster. The mode provides the most frequent category/value; the median provides the middle point/”centre” of the data and bisects the distribution into two equal part; and the mean is the mathematical average of values.
One thing worth repeating is the caveat about the appropriateness of each of the measures of central tendency given the level of measurement of the variables at hand. Below is a quick, “cheat sheet” type of a table summarizing which central tendency measures are appropriate for which levels of measurement.
Table 3.8 What Central Tendency Measures to Report for The Different Types of Variables
| Nominal Scale | Ordinal Scale | Interval/Ratio Scale | |
| Mode | ♦ | ♦ | ♦ |
| Median | – | ♦ | ♦ |
| Mean | – | – | ♦ |
In other words, the mode is appropriate for all variables, regardless of their level of measurement; the median works only with ordinal and interval/ratio variables; and the mean can be calculated only for interval/ratio variables.
I’ll also restate it in terms of the variable type: nominal variables have only a mode; ordinal variables a mode and a median; and interval/ratio variables have all three measures of central tendency.
In terms of working with SPSS, as usual, it is you who makes the decision to request modes, medians, and means. You can either memorize the above Table 3.8, or, better yet, understand the logic behind each central tendency measure to know whether it’s logically possible to apply it to a variable of a given scale — but in either case, SPSS will not make the decision for you.
Watch Out!! #9… for Trusting SPSS to Provide Only Appropriate Measures
SPSS cannot tell you the appropriate central tendency measures for a specific variable. Sometimes, if you make a mistake, depending on the mathematical procedure requested, SPSS might be genuinely unable to execute a command which will alert you to the fact that you have made an error. However, in many cases SPSS will execute a command and will produce output, regardless of whether the command makes logical sense or not.
To your bad luck, the measures of central tendency (and, as we will see in the next chapter, the measures of dispersion) are exactly one of these cases where SPSS will produce any measure of central tendency for any variable you ask of it. Thus, for example, if you request a mean for race/ethnicity, or a median for religious affiliation, it will execute the commands and give you what you asked for: it will produce numbers (which, if you remember, stand for the numerical labels of the categories). It will be then up to you to interpret those numbers.
This, however, would be a logical impossibility — there is no average race/ethnicity, nor “centre value” for religious affiliation. You would have made a mistake, and SPSS would have let you have your meaningless output.
This basically illustrates the saying “garbage in, garbage out”: if you input nonsense, the output will be nonsensical too. It thus falls on you to not input nonsense and to not request measures of central tendency for variables for which they are inappropriate.
Results aside, proper communicating of findings is also very important. Even when output is produced correctly, your job is still not done: you still have to interpret the results and communicate what you have found. Considering that people in general (including in the social sciences) are variously trained in quantitative research, it is always a good idea to “translate” the more technical jargon into a more easily understandable, everyday language.
Specifically about descriptive statistics like the measures of central tendency we explored in this chapter, or the measures of dispersion in Chapter 4, the goal is to communicate your findings not only about variables and measures and modes, etc. but to explain what you have found in terms of people (or whatever units of analysis you happen to work with). Thus, “the mode of religious affiliation is…” becomes “the most frequently reported religious affiliation is…” or even “respondents most frequently identified as … in terms of their religious affiliation”. (As well, getting into the habit of “translating” variable-centric jargon into people-centered statements is a good practice for your understanding of the material.)
Finally, a related issue is remembering to use the variable’s units of measurement when communicating results. To give a few examples, the median of number of siblings is measured in “siblings”, the mean of income is measured in “dollars”, the mode of age is measured in “years”, etc. If you know the unit of measurement of the variable you describe (and you should), use it: a median age is never, say, 20; it’s 20 years.
With this done, we now turn to the last set of measures used to describe variables, namely measures of dispersion.