Question

If an entire population of N = 20 scores is transformed into z-scores, the value of SS, the sum of squared deviations, for the set of 20 z-scores is 20.

a. True
b. False

Answer 1

The statement is true. When a population of scores is transformed into z-scores, the sum of squared deviations for the set of z-scores equals the number of scores in the population.

Step-by-step explanation:

For a set of scores transformed into z-scores, the sum of squares (SS) measures the total variance of a dataset from its mean. By definition, a z-score represents the number of standard deviations a score is from the mean in a standard normal distribution (Z ~ N(0, 1)), with a mean of 0 and a standard deviation of 1.

In transforming any dataset to z-scores, the mean of the dataset becomes 0, and the variance (or the sum of the squared deviations from the mean) becomes 1 for each data point. Since variance is the average of these squared deviations, and in the case of z-scores, each has a variance of 1, the SS for the entire set of scores would indeed be equal to the number of scores, N.

Therefore, if an entire population of N = 20 scores is transformed into z-scores, the value of SS would indeed equal 20 (SS = 20). Hence the statement is true.