Find standard deviation and percentage of sample within given means?

You count the number of beta rays from a 137Cs source. You do this 20 times during the same period of time and find the following number of counts: 1044, 1154, 1106, 1055, 1086, 1112, 1079, 1087, 1079, 1060, 1128, 1059, 1055, 1092, 1038, 1117, 1141, 1083, 1141, and 1128.





a) What is the average number of counts?


1092.2





b) What is the (sample) standard deviation of your sample?


______





c) What percentage of your sample of numbers should be within %26lt; N %26gt; +/-2 sq rt %26lt; N %26gt; ?


______%





FOUND PART a BUT DON'T KNOW HOW TO DO PART b AND c





THANK YOU!

Find standard deviation and percentage of sample within given means?
You're in the wrong category...this is a Mathematics question. The good news is that physicists have all the math to answer.





The standard deviation (SD) is a sort of average, like the mean. The difference is that this is the average of the square of the difference between each data point and the mean. This difference is d = x - m; where x is your data (1044, 1154, ... , 1128) and m is the mean m = 1092.2.





As the average of the square of the difference we find something called the variance, which is just Var = SD^2 = SUM(d^2)/N; where N is the number of data points. If the number of data points is just a sampling of all data points, then for reasons usually uncovered in advanced statistics, we use n = N - 1 to average out the d^2. n is called the degrees of freedom.





So there we have it, the standard deviation is SD = sqrt(SUM((x - m)^2)/(N - 1)); where N = 20 data points and m = 1092.2 counts. Find d = x - m for each data point x, square it and add all the d^2. Then divide that SUM by N - 1. That will give you the variance Var. Take sqrt(Var) = SD.





As to c., if you assume the probability distribution of the sample counts is Normal, then you should know that 95% of your counts will lie between +- 2SD on either side of the mean m. After you find SD, add 2SD to your mean m for the upper bound and substract 2SD from your mean for the lower bound. 95% of all your counts should lie between the upper and lower bounds, which are at the +- 2SD marks.

wallflower