Question

According to the material presented in chapter 5 of Social Statistics for a Diverse Society ed. 8, why do researchers use z scores?

Answer 1

Solution: The z-score is the standardized score and it tells us how many standard deviations above or below a particular value is from the mean. Suppose we have a random variable x = 130 (math score of a student in the class). Let us assume the mean of the math score is 120 with a standard deviation of 10. Now the z-score for the student's score x = 130 is:

Therefore, the z-score of 1 means the student's score x =130 is 1 standard deviation above the mean.

This z-score is also used to find the area under the normal curve. To find that, we first need to determine the z-score and then we need to use the standard normal table (contains pre-calculated z-scores and their corresponding probabilities) to find the required probability.

Hope this helps!