Reading the Histogram, and Understanding Percentile

The interactive model below will be used for most of the activities in the workshop. Let's take a few moments to understand what it's representing. For this activity, we'll be focusing on the graph made up of all the dots and faces.

This graph is meant to represent the students in a school and their scores on a standardized test in math. Here's how to read it. Each dot represents a student. Each number across the bottom represents a score on the test, the number of questions the student got correct.

To make it easier to see patterns, click on the button at the top left of the diagram, 'Kalie's class.' This will make most of the dots disappear, and you'll only see kids with hair -- these are Kalie's classmates. You can also see Kalie, the only kid drawn with eyes and a mouth. Don't click on anything else for now. Okay, so once you've clicked on Kalie's class, you'll see that 2 kids happened to answer 20 questions correct. Kalie got 15 questions right.

Activity

Take a few moments to answer these questions.

• How many other kids got 15 questions right?
• How many questions are there?
• What was the highest number of questions any student aswered correctly? What was the lowest?

Percentile is an important and tricky concept to get a handle on. Many standardized tests give scores in percentiles. Percentiles indicate how well a student did compared to others. If Kalie ranked in the 60th percentile, that would mean that she performed as well as or better than 60% of other students, though in most cases she would have answered more than 60% of the questions correctly.

The test scores shown above are a bit unusual because the 50th percentile happens to correspond with a score of 15 out of 30, or 50% correct. This is not typical for standardizd tests.

Activity

Try this. Find the slider in the yellow square called 'School skills.' Slide it up to the top. You'll see that Kalie's score improves to 17 correct questions. 17 out of 30 is 56% correct, but you can see on Kalie's score report that she's now jumped to the 62nd percentile. Why did her percentile score make such a big jump?