Please help me with this Standard Of Deviation Question?

5 8 11 9 12 5 9 7 3





(a) Calculate the Range





(b) Calculate the Standard Deviation





(c) Calculate the Variance

Please help me with this Standard Of Deviation Question?
a) Range = 9





b) Standard Deviation = 2.958





c) Variance = 8.75





Hope that helps
Reply:a) The range is simply the highest number in the set minus the lowest number in the set. In this case, the range is 12 - 3 = 9





b) The standard deviation is equal to the square root of (sum of all (x - mean)^2 / n)





If this is a sample of data, and not the entire population, you divide by n - 1.





You must calculate the mean first, by adding up all the numbers and dividing by 9.


The mean is approx. 7.67





Now for each individual data point, you must subtract the mean from it and then square the value.





(5 - 7.67)^2 = 7.1289


(8 - 7.67)^2 = 0.1089


(11 - 7.67)^2 = 11.0889


(9 - 7.67)^2 = 1.7689


(12 - 7.67)^2 = 18.7489


(5 - 7.67)^2 = 7.1290


(9 - 7.67)^2 = 1.7689


(7 - 7.67)^2 = 0.4489


(3 - 7.67)^2 = 21.8089





Now add these totals up to get 70.0002.





If you are doing a sample, the Standard deviation is approx. equal to the Sq. root of (70.0002 / 8) = 2.958





If you are doing a population, the Standard deviation is approx. equal to the Sq. root of (70.0002 / 9) = 2.789





c) The variance is equal to the standard deviation squared (don't include the square root sign when calculating standard deviation to find the variance), which for a sample is 8.75 and for a population is 7.7778

hollyhock