Is the second quartile (Q2) always the median?

Question

I'm having a debate with someone outside of work.

Is there a chance where the 50th percentile does not equal to the median?

Have you ever encounter such scenario before? Do you think it is even possible?

Please share your thoughts!

Thank You,
-Sabrina-

sabrinafong8 · Answer

Thank you for your insights, Don!

DonMcCormack · Answer

By definition, the median is the point at which half the data falls above and half below. This is the same definition for the 50th percentile. Algorithmically, you can have different ways to calculate the median (or 50th percentile) if there are an even number of observations. I suppose that you could choose different methods for calculating each statistic, making them different, but that would seem inconsistent.