Chapter 25. Mode, Median, and Mean
Learning Objectives
Understand how simple statistics are used to describe a distribution of scores.
Distinguish the mode, median, and mean in terms of their method of calculation.
Describe the use of the mode, median, and mean in measuring behavioral variables.
Review
Review
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1. When researchers measure some aspect of behavior, they organize the raw scores into what is called a distribution of scores by ranking all the scores from the lowest to the highest, then counting the number of occurrences of each score.
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2. But if the data set is large, researchers find it hard to make sense of these raw scores. Instead, they use special calculated numbers called statistics to describe and interpret their results.
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3. Some statistics are measures of central tendency, a way of describing the typical score that best represents the distribution. The mode (the most frequent score) is the simplest measure, but it is not as useful as the median (the middle score in the distribution).
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4. Researchers generally prefer to use the mean, computed by adding the scores and dividing by the number of scores. This works well with symmetrical distributions such as this one, where the shapes of the left half and right half of the distribution are similar.
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5. But if the distribution has a few extreme scores that pull the mean in their direction, such as a handful of very dedicated runners logging many more miles than typical joggers, researchers would use the median instead.
Practice 1: Building a Distribution of Scores
Practice 1: Building a Distribution of Scores
Select the PLAY button to build the distribution and show how many times each score occurs.
When researchers measure some behavioral variable, they typically construct a distribution that organizes the scores on that variable, and then calculate statistics to describe and interpret the results. First, let's build a distribution and draw a graph of the distribution.
Practice 2: Calculating the Mode, Median, and Mean
Practice 2: Calculating the Mode, Median, and Mean
Select the Calculate buttons to calculate the mode, the median, and the mean of this distribution.
The mode is simply the most frequent score in the distribution. The median is the middle score (i.e., it has an equal number of scores above and below it) in a distribution of sorted scores. The mean is the "arithmetic average," calculated by adding all scores and dividing by the number of scores.
Practice 3: Modifying the Distribution
Practice 3: Modifying the Distribution
Drag one of the green blocks to an available gray area, then observe the change in the statistics.
Here are the statistics for the distribution—the mean, median, and mode. To modify the distribution, drag one of the green rectangular blocks on the graph to a new location (the gray areas). When you release the block, the statistics will be updated to reflect the modified distribution.
Quiz 1
Quiz 1
Match the terms for measures of central tendency to the descriptions by dragging each colored circle to the appropriate gray circle. When all the circles have been placed, select the CHECK ANSWER button.
Quiz 2
Quiz 2
Drag one green block as directed. Next, choose an answer to the question. Then, select the CHECK ANSWER button.
A few extreme scores (on the edges of the distribution) can influence some of the statistics. To observe this, drag the green block for score “5” into the gray area above score “1” and notice which statistic changes the most. Then, answer the question.
Conclusion