the number of times an item was sampled in a given time period.
Sample means are not as random as the number of items per moment when the sample is calculated.
The simplest way to calculate a sample mean is to take any random sampling scheme and simply take the mean of every item that was sampled. The simplest example is probably the coin toss. If you have a coin that comes up heads 50% of the time, and tails 50% of the time, the mean of the two values is 50%. But the number of heads is 50% of the time, and tails 50% of the time, so the mean of the two values is 50%.
But this gets a little weird if you imagine the number of heads is 1.5 times the number of tails. The probability that the number of heads is 1.5 times the number of tails is 1.5. So the probability that the sample mean is 1.5 is 1.5.
This is a little more complicated if you imagine the number of heads is 2.5 times the number of tails. The probability that the sample mean is 2.5 is 2.5. So the probability that the sample mean is 2.5 is 2.5. This is why the sample mean is different from the mean of the sample.
This concept is based on the following thought experiment: Imagine that you are given a sample of 100 people. There is a 50% chance that at least one person is male, and a 50% chance that at least one person is female. Now, imagine that you know that 50% of the people in the sample are male and 50% of the people in the sample are female.
You are going to ask the sample to predict the gender of the next person in the sample. How do you do it? You take the sample mean of the 100 people and add the 50 of the male people to the 50 of the female people. That is the first step.
So, I get it. You are thinking about the sample mean of 100 people. That would mean a 100 person sample and 50 male and 50 female people. So the sample mean is 50 people. 50 people is the sample mean of the people in the sample. Now, the 50 people that are male are the 50 people that are male in the sample. The 50 people that are female are the 50 people that are female in the sample.
The problem is that the sample mean doesn’t tell us the actual total numbers of people in this sample. The sample mean tells us the sample standard deviation, but not the variance. So we can’t really use the sample mean to compare the actual numbers with the sample standard deviation.
As it turns out, the sample means tell us the sample standard deviation instead of the actual number. So as a result, it’s not even clear that the actual number of people in this sample is the sample mean, but rather that the sample standard deviation is what we get when we take the sample means.