find the standard deviation for the following: 8,5, 12, 8, 9, 15, 21, 16, 3. There is a formula but our teacher wants us to do it a specific way.

Question

For example, 47, 41, 32, 53, 57. First you find the mean, which is 46 and then subtract it with each number in the set so you get 1, -5, -14, 7, 11. then you square each # to get 1, 25, 196, 49, 121. then add all the numbers to get 392 & you do 392/n-1 (n being how many #s there are in the set) so 392/5-1 = 98 then you square root 98 & the standard deviation is 9.9.

For 8, 5, 12, 8, 9, 15, 21, 16, 3 the standard deviation is 5.73973 but when i tried the process i get a completely different answer. First the i found the mean, which is 10.77777778. (97/9) but after this i started messing up, help?

Answer 1

mean = 97/9 = 10.78
Sd = sqrt ((x -mean)^2/(n-1)) = 5.7397

correct

Answer 2

how do you do it the way i showed above? because our teacher doesn't want us to use the formula