Brilliant Marathon!

Though it seems like your friend has beaten you, you actually have won. This counter-intuitiveness is called the Simpson's Paradox .

During the first day, you answered $62.2\% \times 1200 \approx 746$ questions right whereas your friend answered $63.6\% \times 700 \approx 445$ questions right.

During the second day, you answered $58.3\% \times 300 \approx 175$ questions right whereas your friend answered $58.8\% \times 800 \approx 470$ questions right.

Furthermore, both you and your friend answered all 1500 of the questions. We will represent the above information in a table.

$\begin{array} {|c|c|c|} \hline \\ & \text{You} & \text{Your friend} \\ \hline \\ \text{Day 1} & 746 & 445 \\ \hline \\ \text{Day 2} & 175 & 470 \\ \hline \\ \text{Total} & 921 & 915\\ \hline \end{array}$

Clearly, you answered more questions correct that your friend. Therefore, you are the winner.

No calculation is required.magnitude of difference in the numbet of questions solved on both days are same.(500 & -500). Just by seeing that average of 62.2 & 63.6 is greater than that of 58.3 & 58.6. We can say you win

I chose "you" without calculation betting on the fact that the example is intended to demonstrate Simpson's paradox ;) the answer should have been misleading...

Apart from percentages, if we look at the sum of the actual number of correct answers, I won

The total questions that I answer correctly is 1200 .622+300 .583 = 921.3 while the correct answered questions by my friend is 700 .636+800 .588 = 915.6. So I win the marathon.

My friend is not that stupid!! Yes Sharky Kesa rightly pointed out that it was a Simpson's Paradox. We get a particular result while doing experiments but the result gets reversed when the sets are combined together!!!

It's now your turn to tease your friend :-) :-)

Do teach your friend the Simpson's Paradox