Question

What are the values for SS (sum of squared deviations) and variance for the following sample of n = 4 scores? Sample: 1, 1, 0, 4

a. SS = 7, Variance = 1.75
b. SS = 10, Variance = 2.5
c. SS = 8, Variance = 2
d. SS = 6, Variance = 1.5

Answer 1

To calculate the sum of squared deviations and variance for a sample, you need to calculate the mean, subtract the mean from each score, square the result, add the squared deviations, and divide by the sample size minus 1.

Step-by-step explanation:

To find the sum of squared deviations (SS) and variance for a sample, you need to follow these steps:

1. Calculate the mean of the sample scores. For the given sample (1, 1, 0, 4), the mean is (1 + 1 + 0 + 4) / 4 = 1.5.
2. Subtract the mean from each individual score and square the result. For example, for the first score 1, the deviation is 1 - 1.5 = -0.5, and the squared deviation is (-0.5)^2 = 0.25.
3. Add together all the squared deviations to find the sum of squared deviations (SS). For the given sample, the SS is 0.25 + 0.25 + 2.25 + 4.25 = 7.
4. To calculate the variance, divide the SS by the sample size minus 1. For the given sample, the variance is 7 / (4 - 1) = 2.33.

Therefore, the correct answer is d. SS = 7, Variance = 2.33.