Quiz 10.1

The sum of the squared deviation scores is SS = 20 for a sample of n = 5 scores. What is the variance for this sample?

Sample variance = SS / (n-1) = 20 / ((5-1) = 20/4 = 5

What is the variance for the following population of scores? Scores: 5, 2, 5, 4

Scores: 5, 2, 5, 4, Mean: (5+2+5+4)/4 = 4 Difference between each score and mean: 5-4=1 2-4=-2 5-4=1 4-4=0 List of squared difference: 1, 4, 1, 0 Sum of squared difference: 1+4+1+0 = 6 Variance = SS/N= 6/4=1.5

A population of N = 100 scores has mean µ = 30 and standard deviation σ = 4. What is the population variance?

The easiest way to find the variance is to square the standard deviation

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

Mean: (1 +1+0+4)/4 = 1.5 Difference between each score and mean: 1-1.5 = -0.5 1-1.5 = -0.5 0-1.5 = -1.5 4-1.5 = 2.5 List of squared difference: 0.25, 0.25, 2.25, 6.25 Sum of squared difference: 0.25 + 0.25 + 2.25 + 6.25 = 9 Variance = SS/n-1 = 9/3=3

What are the values for SS and variance for the following sample of n = 3 scores? Sample: 1, 4, 7

Mean: (1+4+7)/3 = 4 Difference between each score and mean: 1-4= -3 4-4 = 0 7-4 = 3 List of squared difference: 9, 0, 9 Sum of squared difference: 9+0+9 = 18 Variance = SS/n-1 = 18/2 = 9

Which of the following symbols identifies the population standard deviation?

Population standard deviation: o = √o2 = √SS/N

The sum of the squared deviation scores is SS = 20 for a population of N = 5 scores. What is the variance for this population?

Population variance: o = SS/N = 20/5

A sample of n = 9 scores has a variance of s2 = 144. What is the standard deviation for this sample?

Simply take the square-root of the variance to find the standard deviation

A sample of n=8 scores has SS = 50. If these same scores were a population, then the SS value for the population would be _______.

The sum of squared value is the same for population and sample. Variance and standard deviation are different between population and sample due to the difference in the formula.

A population of N = 6 scores has Σ X = 12 and Σ X2 = 54. What is the value of SS for this population?

Using the computational formula for SS: SS = ∑X2 - (∑X)2/N = 54-(12)2/6 = 54 - 144/6 = 54-24 = 30