Methodology Behind Computing 1st and 3rd Quartiles in CODAP

[michaelkaskadamis@gmail.com]

Hello CODAP community,

While analyzing a dataset of numbers ranging from 1 to 11, I observed a distinct approach CODAP employs for computing the 1st and 3rd quartiles. Specifically, CODAP calculates Q1 as 3.5 and Q3 as 8.5, suggesting that the median is counted in both the lower and upper halves for the quartile computations.

I’m aware that there are multiple methods for determining quartiles, and the methodology can vary. However, it’s commonly taught and used for datasets with an odd number of values  to exclude the median when computing Q1 and Q3.

With this context, I’m curious as to why CODAP has chosen to adopt this particular method. Are there specific advantages or underlying reasons for this approach compared to the more conventional one?

Any insights or explanations would be greatly appreciated.

Thank you in advance for your time and clarification.

Best regards,
Michael Kaskadamis

 

[Bill Finzer]

Hello Michael,

Thank you for your question. As you may be aware, CODAP descends from Fathom both in spirit and, in some places, in code. CODAP computes Q1 and Q3 as Fathom does. The decision for both applications is based on the tenet that you should get the same value for each as you get from the function that computes the 25th or 75th percentile. The percentile function takes any number between 0 and 1 for an argument, does not treat 0.25 or 0.75 as special, and always includes all values.

Perhaps the fact that there are multiple multiple methods for determining the quartile values has at least the saving grace of providing an opportunity for students to experience the arbitrariness of some rules and to grapple with a situation in which, at least some would say, there is more than one right answer.

Further thoughts welcome!

Bill

[patkinson@cityneighborshighschool.org]

As a follow up, I wonder if you could recommend a method for having students generate the alternate quartile values, while they are not the percentile values they sometimes are the correct answer for our online problem sets.

[Dan Damelin]

Do these functions work to calculate quartiles in the way you would like? Click on the Q1 or Q3 attributes and select “edit formula” to see how they were written. You can also experiment with changing the list of values to explore varying results calculated from different lists of numbers.

https://codap.concord.org/releases/latest/static/dg/en/cert/index.html#shared=https%3A%2F%2Fcfm-shared.concord.org%2FkQHNnM08vizJca432Jrt%2Ffile.json

• This reply was modified 1 year, 3 months ago by Dan Damelin.

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