A client of mine in Finite Math received the following data and was asked to find the sample standard deviation. (Actually, they don't specify 'sample'. This class doesn't seem to teach population parameters).
I don't know what the data is about except that it has to do with populations which makes sense looking at the numbers, with the categories being age groups. The midpoint and frequency were given in the problem as shown in this first photo.
The student uses a TI-84 and entered the numbers as given. Note that the TI-84 appears to err when given decimal numbers in the frequency column. Using such numbers will output a blank sample standard deviation (s). However, it does output the population standard deviation correctly as 13.95. This was counted wrong though. Apparently, the instructor said the answers was 14 something – probably the 14.67 shown above.
This presents a problem on how I should teach my client to do the problem. Maybe they can use Excel like I've done, but I doubt it. Maybe I can have them convert to whole numbers? Let's see what happens there.
The TI-84 outputs the same numbers for the sample and population standard deviation – 13.95.
Clearly, the number are practically the same because n is so much higher now.
So, let me rephrase the question. If we are to assume that the given frequencies are in millions exactly, then the second image calculation must be the correct one, right?
Best Answer
I think I answered my own question now - the instructor is incorrect. Dividing by ( n-1 ) in the first photo is dividing by 9.4 million. You don't want to do that. You do not have one million degrees of freedom. Also, who has ever taken a sample size of 10.4 million? Even, if you somehow did that is such a large sample that the standard deviation is essentially the same as the population standard deviation, as shown in the second photo.