However, the key finding is that Sarah's score was not one of the best marks. Hence, 24.86% of the scores (0.2486 x 100 = 24.86%) were lower than Sarah's, but above the mean score. We can also see how well she performed relative to the mean score by subtracting her score from the mean (0.5 - 0.2514 = 0.2486). What Altman did was calculate the Z-score by weighting several. Going back to our question, 'How well did Sarah perform in her English Literature coursework compared to the other 50 students?', clearly we can see that Sarah did better than a large proportion of students, with 74.86% of the class scoring lower than her (100% - 25.14% = 74.86%). You subtract the mean from the total score and then divide that by the standard deviation. In other words, around 25% of the class got a better mark than Sarah (roughly 13 students since there is no such thing as part of a student!). If we look at this as a percentage, we simply times the score by 100 hence 0.2514 x 100 = 25.14%. This means that the probability of a score being greater than 0.67 is 0.2514. Therefore, we start with the y-axis, finding 0.6, and then move along the x-axis until we find 0.07, before finally reading off the appropriate number in this case, 0.2514. The y-axis in the table highlights the first two digits of our z-score and the x-axis the second decimal place. Z-scores will measure the exact amount of standard deviations above or below the population mean for each data point. It does this by converting (or standardizing) the raw scores in a normal distribution. Once you input this information, the calculator does the rest of the work for you. It takes in three pieces of information: the population mean, the population standard deviation, and a value you want to calculate the z-score for. To use the table, which is easier than it might look at first sight, we start with our z-score, 0.67 (if our z-score had more than two decimal places, for example, ours was 0.6667, we would round it up or down accordingly hence, 0.6667 would become 0.67). A z-score, or standard score, is a numerical value that measures the standard deviation units between a data point and the population mean. A z-score calculator is a tool that allows you to easily calculate z-scores.

This table helps us to identify the probability that a score is greater or less than our z-score score.

Compute z score