I have two relative frequencies for the same experiment done twice. A fair coin's been flipped 100 times with 56/100 as the relative frequency of Heads, and 500 more times with 252/500 as the relative frequency of heads.
I'm now being asked the average relative frequency. Shouldn't that just be 306/600? Apparently that one's not right. What am I doing wrong here - I can't see anything about average relative frequency on google?
Even though I agree that 306/600 is a closer estimate to the actual probability of heads, we have to consider another possible interpretation of "average relative frequency", which could be the literal average, namely,
(50/100+252/500)/2
= 251/500.
Have you tried that option?
That one works, thank you! Didn't consider actually getting the average properly, whoops.
You're welcome! Glad that it works out.
To calculate the average relative frequency, you need to consider the total number of trials and the total number of successful outcomes across all experiments.
In this case, you conducted two experiments: one with 100 coin tosses and another with 500 coin tosses. For the first experiment, the relative frequency of getting Heads was 56/100, and for the second experiment, it was 252/500.
To find the average relative frequency, you need to calculate the total number of successful outcomes and the total number of trials.
For the first experiment, you had 100 trials and 56 successful outcomes (Heads). For the second experiment, you had 500 trials and 252 successful outcomes.
To find the average relative frequency, add up all the successful outcomes and divide it by the total number of trials:
(56 + 252) / (100 + 500) = 308 / 600
So the average relative frequency is 308/600, rather than 306/600.