Similarly, a z score of -1 tells you that the observation is one standard deviation towards the left of the center.
A z score of 1 tells you that the observation is at a distance of one standard deviation towards the right from the center. In more simple terminology, the standard score tells you how far an observation is from the average of the data in terms of standard deviations. In other words, it should tell the instructor whether a score of 75 is in the top 10% of the class or not. Using a z table, you can obtain the corresponding p value test statistic for this z score, and the p value here should tell you what the chances are for someone in the class to score more than 75 marks in terms of probability. This turns your raw score into a standardized score (which can be used to calculate tail probabilities for hypothesis testing). Using the given information, the instructor can find the standard score using the z score calculation formula. In the beginning, this may seem like a tedious calculation, but the zscore test statistic makes it fairly easy. Now suppose the instructor is interested in knowing whether one of his best students who scored a 75 is among the top 10% of the scorers. Suppose you have the distribution of class grades for an exam that appears to be normal and it has a mean of 45.
#Z score table how to
You can read more about p-values and how to find them with contingency tables here.