\nStatistics focuses on the mean and the standard deviation. But why is that? The reason is that while most phenomena follow a normal distribution, very few follow the standard normal distribution. Yet, the standard normal distribution is what we have tables for.<\/p>\n
The z-score of a measurement “standardizes” it; i.e., it tells where that measurement would fall in the standard normal distribution, based on its placement in its own distribution.<\/p>\n
The z-score of measurement x is given by <\/p>\n
z=(x-\u03bc)\/\u03c3<\/span><\/p>\n where<\/p>\n \u03bc = mean of population x is from Example:<\/strong><\/p>\n Find the z score of the exam mark 72 if the mean mark is 61 and the standard deviation is 12.<\/p>\n Solution:<\/p>\n z = (x-\u03bc)\/\u03c3 = (72-61)\/12 = 11\/12 = 0.9167<\/p>\n Looking at a z-score table or else the Sharp EL-520W (see here<\/a>), we get the answer 0.82035: 82% of the students got that mark or below. Therefore, only 18% got above it.<\/p>\n z-scores can be seen as leading to the “bell curve” people refer to in connection with exam marks.<\/p>\n HTH:)<\/p>\n
\n\u03c3 = standard deviation of the population x is from<\/p>\n