Chapter 5. Sensation and Perception

Statistical Concepts Covered: In this applet we will discover how to summarize data distributions using measures of central tendency and variability, and learn why picking the right summary statistics is critically important when describing data.

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Statistical Lesson. It may come as a surprise to learn that more than half of the values in a distribution can be below average. In a skewed distribution, the mean value is pulled toward the tail and more than half of the values—and sometimes far more than half of the values—can be above or below the average. In such situations, the mean value may not be the best representation of the entire data set. We will explore this concept more in the following questions.

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Statistical Lesson. You may sometimes hear friends or even professors say something like “75% of all students think that they are above average!”, implying that such a distribution is not possible. In fact, it is possible, and it is not even unusual. Whenever you are dealing with a negatively skewed distribution, the mean value is pulled toward the tail, and more than half of the values—and sometimes vastly more than half of the values—can be above the mean (“above average”). For the “strongest pain experienced” data, approximately 55% of the responses are above the mean value. In most Introductory Psychology classes, the exam scores are negatively skewed, so it’s quite likely that far more than half of your classmates will have an above-average score on the next exam!

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Statistical Lesson. Another very important aspect of describing data distributions is indicating the variability, or how “spread out” the data are. If we collected data on the ages of the students in your Introduction to Psychology class, there may be a few people who are several years younger or older than the others, but for the most part we would expect the ages to be grouped into a fairly tight range between perhaps 18 and 23 years old. Because the ages are mostly grouped together, we would say that these data have a low variability. But now suppose we asked the members of your class to report the size of their high school graduating class. In this case, we would expect to get a much larger range of answers: Some students may have come from schools with only 20 or 30 graduating seniors, whereas others may have graduated with 2,000 or more other students. Because these values are so spread out, we would say that the data set has a much higher variability. Variability is key concept in statistics, and the next questions will introduce one commonly used measure of variability, the standard deviation of the data.

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