# Percentiles and Distributions

Last Updated: March 21, 2019# Percentiles and Distributions

Mark Espinola, CEO + Co-founder at GradeHub, recently spoke with Dr. Jennifer Balogh about her book.

*An edited transcript of the conversation follows.*

**Mark Espinola:** Hi, this is Mark from GradeHub. I’m here with Jennifer Balogh, a testing expert and author of *A Practical Guide to Creating Quality Exams*. If you missed our last segment on Validity, Reliability, and Overall Exam Statistics, please check that out. With this installment, we’re discussing percentiles and distributions.

Jennifer, thanks for joining me.

So Jennifer, why should an instructor review distributions and percentiles for her exam?**Jennifer Balogh**: Percentiles and distributions give you a lot of information about what is the spread of the students across the different scores. Both percentiles and distributions can be useful for a lot of different reasons.

- One, a lot of people use percentiles for interpretation. Students, for example, they want to know … “was I near the middle of students, above average or below average?” Percentiles and the general distribution will help students understand where they are so that they can monitor their learning and try to shoot for the upper half of the distribution of students.
- The other thing that teachers sometimes use percentiles for is grading. Percentiles are very useful, for example, if you’re grading on the bell curve because it provides a lot of the computations that you’re going to use for that kind of scoring.

## “Percentiles and distributions give you a lot of information about what is the spread of the students across the different scores.”

**Mark: **So how are distributions and percentiles similar and how do they differ?**Jennifer:** A distribution is how many students are scoring at a certain level on your test. A percentile is quantifying that by showing you the percentage of scores of the students that performed at a particular score or lower.

**Mark: **Okay, as in our last installment, can you go through GradeHub’s percentile report so we can learn how you would interpret these results?

**Jennifer:** Sure, I love the clarity in the percentiles graphic in GradeHub. It’s great to see the distribution at a glance. I think that’s a very nice representation there.

Going from left to right, you see on the left is the score as a percentage. Next is the number of points.

Then what you see on the student column is the frequency of students who scored a certain number of points. It can give you an idea of where the middle tendency is with the highest point on that distribution being called the mode. You can see by looking at the student column that six people scored 17 points. So that’s going to be the mode of your distribution. The student column is another way of trying to understand where is the middle. It’s good for you to know the middle to see if students performed generally well or not so well on the test.

## “You can see by looking at the student column that six people scored 17 points. So that’s going to be the mode of your distribution.”

The next column is the cumulative percent. That’s going to give you an idea of how many students and what percent of students scored at a certain level and how many students are below that level, counting up.

Last, you’ve got percentiles in the rightmost column. There again, you are looking at the percentage of students who achieved a certain score, the percentage of those students, and all the students below them. Here, you can see the 50th percentile is somewhere in between 16 and 17 points in this example.

**Mark: **Interesting, I never thought of using percentiles to figure out where the middle of your classes resides.

**Jennifer**: Yes, because you’re right, and that you can see that reflected in the median as the middle score, so it is the 50th percentile.