5.1: What is Central Tendency? Why Do We Use It?

We use central tendency because when we collect data, we have a series of numbers. We call that series of numbers a dataset. These numbers are our observations of that “it” that is varying. This series of numbers is all over the place. There are likely several of them; they are taken in different contexts, and their range can be anything. It’s a lot of information to process. What do we do?

Recall that descriptive statistics is the first step of any statistical analysis; its purpose is to describe the data. What we do is find a way to summarize all that data and organize it. This process is often called summary statistics, and it is just another name for descriptive statistics. There are no strict definitions or distinctions between descriptive and summary statistics. For the purpose of this chapter, I will state that descriptive statistics is a process of describing the variation in our data, and summary statistics is the process of simplifying and organizing the variation in our data.

Data are observations of one “it” at one instance and one point in time. We rarely rely on just one observation of “it.” Even in carpentry and clothes tailoring, we “measure twice, cut once.” We do this because we know that one number, one data point, does not represent “it.” We know that we take a temperature reading and that temperature can fluctuate within the hour. We know that one data point does not represent everything or everybody because not everyone and everything has the same score. The number that represents “it” can fluctuate with another observation of “it.” That’s why we “measure twice, cut once” because our measurement of “it” can be slightly off. We usually take multiple observations of “it,” and that process results in a dataset.

What do we do with that data? Because that is a lot of data to process, we find a way to do something with it. What we do is summarize. Or reduce all these numbers to just a few numbers. We want those numbers to describe the variation. It is just easier to understand a few numbers than to look at all the data at once.

The overall family of values we use for summary statistics are a) central tendency and b) measures of dispersion. Remember: A parameter is a characteristic that describes the normal distribution. Instead of looking at pictures of distributions or a sea of data, a simpler way of describing the distribution is to obtain two values, the central tendency and dispersion. The common terms for central tendency and measures of dispersion are a) the mean and b) the standard deviation. In this chapter, I will focus on central tendency.

Why do we use central tendency?

Central tendency is a statistic that tells us where the scores of a sample are converging. Just to mention here, statistics are values that describe our data. In this case, the value of the statistic describes something about our data. The key issue with central tendency statistics is the term “converge,” which means the tendency, the trend, of where we expect scores to be.

Central tendency helps us do several tasks in statistics.

The central tendency is regarded as the middle, the starting point. Recall that statistics is about the study of variation, and the only way to get variation is to compare “it” with another “it.” You compare something to something. In this case, what we are doing is comparing our observation with the central tendency or the mean. The mean is our starting point for comparison. That’s one reason why we are keen on establishing the central tendency in our sea of varying data.

The measure of central tendency allows us to use one number, for example, the mean, to indicate the performance of the group, otherwise known as the sample.

The term “central tendency” is important as a description of variation because we need the central tendency to establish a focal point in the variation. This focal point is important because most people have scores around the central tendency or the mean. The area where the most scores are at is the hump in the middle of the normal distribution. It is where we will see the majority of scores clump around the mean.

With this focal point as our central tendency, we can address many questions. We need that focal point to indicate where most people will have scores because it helps us determine the significance. The focal point, or central tendency, is our way of comparing what is expected and what is unexpected. The mean is the point where we find the expected scores. Very few people score much higher or lower than the mean.

The central tendency is good for prediction or forecasting. If we do not know what will happen next or what the next data point will be, it is good to use the mean as a predictor of the next data point. The mean is a good summary of what happened before, and what happened before predicts what will happen next. In terms of sampling, the mean is a good indication of how the sample performed, and the mean is a good indication of how the next participant we sample will perform. For example, if we take a sample of fifth graders in a classroom and measure their reading level, we produce a mean reading level score. Then, the next fifth grader enters the classroom, and we measure their reading level. Without any other information at our disposal, our best guess, or estimate, of what the reading level score of that fifth grader will be is the classroom mean score. Central tendency represents our best guess as to what score will occur, which is the central tendency score (e.g., the mean).

The central tendency is good for making comparisons, usually across groups or at different points in time. We can simplify the comparison of two more groups by comparing their central tendency or mean scores. Instead of comparing everyone to everyone, just compare the means. Compare the mean of group A to the mean of group B. Simple. We use this process ubiquitously in psychology research; we compare the means of males to females, treatment versus control, and people who have trauma to people who do not have trauma. We use the same procedure for making comparisons over time. We compare the mean of a group at time one to the mean of the group at time two. Just like for groups, we use this process in psychology research. We want to see how a group performs at intake, then at discharge, then three months later as a follow-up. We want to see how adolescents develop their emotional awareness in sixth grade, then eighth grade, then tenth grade, and then at graduation. The point is this: To simplify your understanding of psychological research and its findings, all we do when we compare groups or something over time is compare the mean scores. Nothing more.