Statistical Analysis: Sum of Squares (SS) and Variance Calculation
What are the values for SS and variance for the following sample of n = 3 scores? Sample: 1, 4, 7
a. SS =18 and variance = 6
b. SS =18 and variance = 9
c. SS = 66 and variance = 33
d. SS = 66 and variance = 22
Answer
The sum of squares (SS) for the scores 1, 4, 7 is 18, and the variance is 9.
To calculate SS, which stands for sum of squares, and variance for a series of scores, we first need to calculate the mean of the scores. For the sample 1, 4, 7, the mean is calculated as (1+4+7)/3 = 4. Next, we subtract each score from the mean and square the result. So, (1-4)^2 = 9, (4-4)^2 = 0, and (7-4)^2 = 9. The sum of these squared differences is the SS. Hence, SS = 9+0+9 = 18. The variance is calculated by dividing SS by n-1 (where n is the number of scores). So, the variance is 18/(3-1) = 9. Therefore, the correct answer is option b: SS =18 and variance = 9.
Statistical analysis involves various calculations to understand and interpret data. Knowing how to calculate SS and variance is essential in analyzing data accurately.
Understanding the concepts of sum of squares and variance can help in making informed decisions based on data analysis results.