Finding the first and third quartile of a box plot I am a bit confused right now because I am doing some practice box plot questions and I came across this particular one. Given the data 1,2,3,4,5,6 I found the following: Median: 3.5 Minimum: 1 Maximum: 6 First quartile: 2 Third quartile: 5 However, this is incorrect and the answer key has the first quartile as 1.75 and the third as 5.25, can someone explain to me how those numbers appeared?

So, the example I found on Wikipedia with $6$ elements looked like this:

Ordered Data Set: $7, 15, 36, 39, 40, 41$. As there are an even number of data points, all three methods give the same results(You can find the methods in my link) $\rightarrow Q_1=15, Q_2=37,5, Q_3=40$. As you can see, $Q_1$ is the second element, $Q_2$ is the median itself, and $Q_3$ is the fifth element.

In your case, your set: $1,2,3,4,5,6 \rightarrow Q_1= 2, Q_2= 3,5, Q_3= 5$, from the same logic.

Your solution seems fine!