Ok, so I have to calculate the arithmetic means of a number of sets each with a number of data points, but I want each mean to be adjusted for reliability based on how many data points I have.
Ex.: say I have a number of values from 1 to 5, so the average is 3. For one set, I have ten values with an arithmetic mean of 3.2, and another with fifty values giving the same mean (3.2). I want a way to show that the second one is more reliable due to the greater number of data points. I'd think the former value should be adjusted towards the average (3), same with values below the average, but I have no idea how to do this rigorously.
Is there a way to do this ? I don't even know how to call it.
Ex.: say I have a number of values from 1 to 5, so the average is 3. For one set, I have ten values with an arithmetic mean of 3.2, and another with fifty values giving the same mean (3.2). I want a way to show that the second one is more reliable due to the greater number of data points. I'd think the former value should be adjusted towards the average (3), same with values below the average, but I have no idea how to do this rigorously.
Is there a way to do this ? I don't even know how to call it.
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