Calculate SS, variance, and standard deviation for the following sample of n=9 scores:2,0,0,0,0,2,0,2,0.(Note: The computational formula for SS works best with these scores.)
I keep getting the wrong numbers. Thank You.
Please define SS.
sum of squares
SS=E(x-u)squared in greek of course
I get:
u=.66666667
ss=8
v=1
sd=1
Note that I am using the formula for the estimate of the variance from a sample. So, I devide by n-1.
To calculate the Sum of Squares (SS), Variance, and Standard Deviation for the given sample, follow these steps:
Step 1: Calculate the Mean of the sample.
Mean = (2 + 0 + 0 + 0 + 0 + 2 + 0 + 2 + 0) / 9 = 0.4444 (rounded to four decimal places)
Step 2: Calculate the Squared Deviations from the mean for each score.
Squared Deviation = (score - Mean)^2
For the given sample, the Squared Deviations are as follows:
(2 - 0.4444)^2 = 1.7760
(0 - 0.4444)^2 = 0.1975
(0 - 0.4444)^2 = 0.1975
(0 - 0.4444)^2 = 0.1975
(0 - 0.4444)^2 = 0.1975
(2 - 0.4444)^2 = 1.7760
(0 - 0.4444)^2 = 0.1975
(2 - 0.4444)^2 = 1.7760
(0 - 0.4444)^2 = 0.1975
Step 3: Calculate the Sum of Squares (SS) by adding all the Squared Deviations together.
SS = 1.7760 + 0.1975 + 0.1975 + 0.1975 + 0.1975 + 1.7760 + 0.1975 + 1.7760 + 0.1975 = 6.2630 (rounded to four decimal places)
Step 4: Calculate the Variance.
Variance = SS / (n - 1) = 6.2630 / (9 - 1) = 0.7829 (rounded to four decimal places)
Step 5: Calculate the Standard Deviation by taking the square root of the Variance.
Standard Deviation = √0.7829 ≈ 0.8842 (rounded to four decimal places)
So, the SS is 6.2630, the variance is 0.7829, and the standard deviation is approximately 0.8842.