finding normal distribution?

Question

I have 2 data sheet each one has an column of numbering data i should calculate from a normal distribution with some unknown mean and unit variance
how can i do it?

Answer 1

If you have data (normal distribution) with unit variance (s^2 = 1). and you need to find the mean, it is easy. The mean is the average over all you data. To find the mean in Excel you can apply the function average(), or you can simply sum up all data and divide by the number of items.

If you need to generate data (numbers) that are normally distributed with mean = 0 and variance = 1, then in Excel you use function RAND() to generate two random numbers R1 and R2. Then your random variate X = sqrt(-2*ln(R1))*cos(2*pi*R2) has a standard normal distribution. To have the variate Y with the same distribution and mean m you calculate Y = m + X.

Answer 2

I'm not sure if I understand your question. But you mean you have to produce the data, or you already have had the data?



In any case, there are various softwares that allow you to do it. For example,



MS Excel: you use the function "NORMDIST"

It returns the normal distribution for the specified mean and standard deviation.



Syntax



NORMDIST(x,mean,standard_dev,cumulative)

X is the value for which you want the distribution.

Mean is the arithmetic mean of the distribution.

Standard_dev is the standard deviation of the distribution.



You can also use Origin by www.originlab.com or Mathematica by Wolfram Research.

If you know how to program, for example in C language, you can also use the random number generator: gasdev(long *idum) by the Numerical Recipes team (www.nr.com).



If I understood more about your question, I would be able to give you a more specific answer.

Answer 3

My interpretation of your question is that you have a lot of numbers that represent measurements of something (your test data) and need to calculate the mean and standard deviation for this data.



The mean is just the average of all the numbers. So, add up all your measurements and divide by the number of measurements you have.



The standard deviation looks more complicated, but it is just more number crunching. Step 1: Find the difference between each measurement and the mean (which you have already calculated) and square it. Step: 2: Add up all the squares - you have one for each measurement. Step 3: Divide the number you just calculated by one less than the number of measurements. Finally, step 4: Take the square root of this number. That is your standard deviation.



To see this written as an equation, go to the following Web site:



http://en.wikipedia.org/wiki/Standard_deviation