Measures of Central Tendency

Updated: Nov 10

Video Transcript

HI! I’m Matthew Courtney, I am an educational researcher and data consultant specializing in data use for continuous improvement in schools. In this video, I am going to introduce you to measures of central tendency and discuss some of their uses in analyzing student data.

You may be asking, what are measures of central tendency anyway? These are measures that help us summaries a distribution of scores – such as the test scores you collected at the end of your last unit. These measures are part of a category of statistics we call “descriptive statistics” because they help you easily and quickly describe a set of student scores to stakeholders and allow for quick comparisons between groups. They are fast to calculate and easy to understand – making them a natural starting place for new data analysists. The three common measures of central tendency are mean, median, and mode.

Let’s start with the mean. You probably know mean better by its other name – average. The mean, or average, helps you know roughly where most of your students performed within a set of scores. Generally, when data is normally distributed, roughly 2/3 of your students will score near the mean. We will talk about this phenomenon more in another video on standard deviation. The mean is generally near the middle, but not always, and its relationship to the middle of a distribution can provide some quick insight into your student performance. The mean is easily calculated in most spreadsheet software using the =AVERAGE formula.

The median is the score in the exact middle of a distribution when you put all of your scores in order. If you do not have an exact middle, then the median is the average of the two scores closest to the middle. The median is helpful when viewed along with the mean because it helps you know if your data is skewed. Generally, if the median is higher than the mean, that means that more kids scores below the middle score than above it. Conversely, if the median is lower than the mean, more kids probably scored above the middle score. Extreme scores can sway this outcome – another issue we will tackle in a different video. To calculate the median in most spreadsheet software, just highlight a set of scores and use the =MEDIAN formula.

The mode is the score, or scores, that shows up most often in a distribution. Distributions can be unimodal, meaning that they have one mode, bimodal, meaning that they have two modes, or multimodal, meaning that they have more than two modes. Some distributions will not have a mode. This is more common in small distributions with a wide range – such as the scores earned on a 100 point test by five students. In spreadsheet software, you can find the mode using the =MODE formula.

Okay – so let’s get out of the theory and take a look at an example of these measures of central tendency in action. Mr. Sanchez just finished grading his latest unit test. He has been asked to present information about his unit test to his colleagues at his professional learning community meeting this afternoon. Mr. Sanchez teaches 173 students in six sections of Algebra I. To prepare for his PLC meeting, he quickly calculates the three measures of central tendency for each of his six sections and makes a report to share during the meeting.

Mr. Sanchez’ data probably looks something like this. He has a column for each of his six sections of Algebra I. I have removed the student names for brevity. I have also condensed the data set – displayed on the screen with the squiggly lines.

Here is the mean, median, and mode for each of his six classes. What do you see? First, we can see that the average performance for his students is in the mid to low sixties… there is probably some re-teaching that needs to happen. Which classes should he be most worried about? The answer may be deceptive. Section 3 appears to be outperforming the other sections – but a high median suggests that more students are scoring on the low-end of the spectrum. Section 5 shows the opposite phenomenon, with more students performing above the mean than below. The class to worry about here is Section 6. They have a low mean that is far below the median. Section 6 also has a very low mode or 31 percent. There are definitely some kids falling behind in Section 6!

Now, take some time to practice the skills we have talked about in this video. First, access the data from a recent assessment from your class. Check to make sure your data is tidy and ready to go. If you are unsure how to do that, check out my video on tidy data. Next, use the formulas discussed in this video to calculate the measures of central tendency for your data. Alternatively, you can upload your data into the free data analysis tools available on my website – Finally, spend some time reflecting on your calculations. What do they tell you about your students’ performance?

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