Alex V. answered • 09/14/21
PhD student with lab experience and 5+ years of teaching experience
Let's start with the mean. To calculate the mean of a sample, we just need to add all the items together, and then divide by the sample size. So, for example, if we're looking for the mean of regular oreo mass, we have a sample of measurements: {14.93, 14.73, 14.83, 14.53, 14.7, 14.22, 14.82, 14.82, 14.81, 14.89, 14.59, 14.68}. To find the mean, we add each of those numbers together, then divide that sum by 12, because there are 12 numbers in the sample.
That leaves us with the Standard Error of the mean and the Standard Deviation. The standard deviation of a sample is a measurement of how "spread out" the numbers are. For example, {1, 9} and {4, 6} have the same mean (5), but the first sample is much more "spread out," i.e. the numbers are farther from the mean than the are in the second sample.
Standard error, on the other hand, is a measure of how likely the mean of our sample is likely to differ from the actual mean of the population we are sampling from. So the standard error of your first oreo example is a measurement of how far the mean of our sample of 12 oreos differs from the mean mass of ALL oreos of that kind.
To find the standard deviation, we first need to calculate the difference between each measurement in our sample and the sample's mean. Then we square that number, then divide it by n-1, where n is the sample size (so for your first oreo case, that's 12). This number is the Variance of our sample. The standard deviation is the variance squared, so to find the SD we just need to take the square root of the variance, which we just found!
With the standard deviation, we can easily find the Standard Error. it's simply the number we got for our standard deviation divided by the square root of n, where as above, n is our sample size.
Hope that helps!
