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.

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?

mean = 97/9 = 10.78

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

correct

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

To find the standard deviation using the specific method your teacher wants you to follow, you need to correctly apply each step.

Step 1: Find the mean.
The mean is the sum of all the numbers divided by the total count of numbers.

For the set 8, 5, 12, 8, 9, 15, 21, 16, 3:
Sum of the numbers = 8 + 5 + 12 + 8 + 9 + 15 + 21 + 16 + 3 = 97
Total count of numbers (n) = 9
Mean = 97 / 9 ≈ 10.778 (rounded to three decimal places)

Step 2: Calculate the deviations.
Subtract the mean from each number in the set.

For the given set, the deviations are:
8 - 10.778 = -2.778
5 - 10.778 = -5.778
12 - 10.778 = 1.222
8 - 10.778 = -2.778
9 - 10.778 = -1.778
15 - 10.778 = 4.222
21 - 10.778 = 10.222
16 - 10.778 = 5.222
3 - 10.778 = -7.778

Step 3: Square each deviation.
Square each of the deviations you calculated in step 2.

For the given set, the squared deviations are:
(-2.778)^2 ≈ 7.721
(-5.778)^2 ≈ 33.453
(1.222)^2 ≈ 1.494
(-2.778)^2 ≈ 7.721
(-1.778)^2 ≈ 3.163
(4.222)^2 ≈ 17.829
(10.222)^2 ≈ 104.574
(5.222)^2 ≈ 27.275
(-7.778)^2 ≈ 60.548

Step 4: Add all the squared deviations.
Sum up all the squared deviations from step 3.

7.721 + 33.453 + 1.494 + 7.721 + 3.163 + 17.829 + 104.574 + 27.275 + 60.548 ≈ 263.777 (rounded to three decimal places)

Step 5: Divide the sum by (n - 1)
Divide the sum of squared deviations from step 4 by (n - 1), where n is the total count of numbers.

In this case, n equals 9, so divide 263.777 by (9 - 1) = 8.

263.777 / 8 ≈ 32.972 (rounded to three decimal places)

Step 6: Take the square root.
Take the square root of the result from step 5.

√32.972 ≈ 5.739 (rounded to three decimal places)

Therefore, the standard deviation for the set 8, 5, 12, 8, 9, 15, 21, 16, 3 is approximately 5.739 using this specific step-by-step method.