Question

Calculate Ss, variance, and standard deviation for the following sample of n = 9 scores.

4, 16, 5, 15, 12, 9, 10, 10,9
Note: The computational formula works best with these scores.
SS:___
Variance: ___
Standard deviation: ___

Answer 1

To calculate the SS (Sum of Squares), variance, and standard deviation for a sample, calculate the mean, find the squared deviations, sum the squared deviations, divide by the total number of scores minus 1 to find the variance, and take the square root of the variance to find the standard deviation.

Step-by-step explanation:

To calculate the SS (Sum of Squares), variance, and standard deviation for a sample, follow these steps:

1. Find the mean of the sample by adding all the scores and dividing by the total number of scores: mean = (4 + 16 + 5 + 15 + 12 + 9 + 10 + 10 + 9) / 9 = 10
2. Subtract the mean from each score to get the deviation from the mean for each score. Calculate the squared deviation for each score: (4-10)^2 = 36, (16-10)^2 = 36, (5-10)^2 = 25, (15-10)^2 = 25, (12-10)^2 = 4, (9-10)^2 = 1, (10-10)^2 = 0, (10-10)^2 = 0, (9-10)^2 = 1
3. Find the sum of the squared deviations: SS = 36 + 36 + 25 + 25 + 4 + 1 + 0 + 0 + 1 = 128
4. Find the variance by dividing the sum of squared deviations by the total number of scores minus 1: variance = 128 / (9-1) = 16
5. Find the standard deviation by taking the square root of the variance: standard deviation = sqrt(16) = 4