Convergence in mean

Imagine you have two groups of people who are measuring how fast they can run around a track. One group measures their times 10 times and gets an average time of 30 seconds. The other group measures their times 100 times and also gets an average time of 30 seconds.

Now, if we compare these two groups in terms of convergence in mean, it means that we're looking at how close their average times are to the actual average time. If we were to repeat these experiments many times, we would expect the average time for both groups to get closer and closer to the actual average time of all runners combined.

Convergence in mean is important because it helps us determine how reliable or accurate our measurements are. If we measure something many times and get similar results each time, we can be more confident that our measurements are accurate.

In summary, convergence in mean refers to how close the average value of measurements from different groups or experiments are to the actual value. The closer they are, the more reliable our measurements are.