Question 536999: The following data lists the average monthly snowfall for January in 15 cities around the US:27 30 30 30 24 21 15 239 35 42 1 1 41 38Find the mean, variance, and standard deviation. Please show all of your work.
PLEASE PLEASE HELP :/
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Your list seems to have 14 numbers, with one of them being 239. You may have meant to write 23 and 9 as separate numbers, or maybe 2 and 39. Not knowing the exact numbers, I could still tell you about calculation procedures.
The website mathisfun describes the theory basics in very simple, easy to understand terms.
Nowadays most calculators can calculate statistics for you. There are also computer programs, like Excel that will do it. Due to differences between calculator models and brands, I cannot explain how to do it in your calculator.
I prefer to use Excel. There have been many versions of Excel, but I don't hink they have changed the names of the functions. You would use the functions named AVERAGE, VARP, and STEDP. Those divide by the number of values you entered (N). Do not use VAR and STDEV, because those divide by (N-1), and they are intended to estimate the spread of all possible values from a smaller sample of them.
Excel even has the functions SUM (sum of all the values) and DEVSQ (sum of squares of differences of the values minus the average, which divided by the number of values gives you the variance).
In the old times (before calculators), calculating variance and standard deviation with just pencil and paper was the only possibility. It used to be a lot of work. I know it well, I was there. We would put the values in a column on one of those accounting notebooks and add them. We would divide the sum by the number of values to find the mean (also called average). We would square each number to get values that we would write to the right, forming the squares column. We would add up that column too, and divide the sum by the number of values to find the average of the squares. Then we would calculate the variance as the average of the squares minus the square of the average. (That is not the calculation as per the definition, but it is mathematically equivalent and easier to do). Finally we would calculate the square root of the variance, which is the standard deviation.
For the numbers 27, 30, 30, 30, 24, 21, 15, 23, 9, 35, 42, 4, 4, 41 and 38, I get sum=373, average=24.8667 (rounded), sum of squares=11427, average of squares= 761.8, DEVSQ=2151.733 (rounded), variance=143.4489 (rounded), standard deviation =11.98 (rounded).
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