The sum of the squared deviation scores is SS = 20 for a population of N = 5 scores. What is the variance for this population?
a. 4
b. 5
c. 80
d. 100
When you find the sum of the squares, divide that by the number of scores to get variance.
Would A be the right answer?
To calculate the variance for a population, you need to follow these steps:
Step 1: Calculate the mean of the population.
Step 2: For each score, calculate the deviation by subtracting the mean from the score.
Step 3: Square each deviation.
Step 4: Sum up all the squared deviations.
Step 5: Divide the sum of squared deviations by the total number of scores in the population.
In this case, the given information is that the sum of squared deviation scores (SS) is 20 for a population with N = 5 scores.
Step 1: Since the mean is not given, let's assume the scores are evenly distributed, and calculate the mean as the average of the scores:
mean = sum of scores / N = SS / N = 20 / 5 = 4
Step 2: Calculate the deviation for each score:
deviation = score - mean
Step 3: Square each deviation:
Squared deviation = deviation^2
Step 4: Sum up all the squared deviations:
SS = sum of squared deviations
Given that SS = 20, the sum of squared deviations is already given.
Step 5: Divide the sum of squared deviations by the total number of scores:
Variance = SS / N = 20 / 5 = 4
Therefore, the variance for this population is 4.
Therefore, the correct answer is:
a. 4