This is because percentiles tend to compress the tails of the distribution, making extreme data values closer together than they actually are.įor example, a male adult height distribution has a mean of 69 inches and a standard deviation of 3.85. When a percentile is known, the corresponding raw data value can also be determined by finding the corresponding z score to the given percentile and then using the equation x = zSD + M.Īlthough percentiles are easy to understand, they can lead to some distortions. In the last two percentile columns, from the 51st percentile and up, are all positive z scores.įinding Raw Data Values Using Percentiles and the z Score Equation This reinforces the fact that z scores that fall below the mean, or the 50th percentile, are negative. Notice that all percentiles in the first two columns have a negative z score. Next to each percentile is its corresponding z score. However, since this conversion from percentile to z score is important when doing z score and T score problems, a percentile table has been made. Any percentile can be converted into its corresponding z score by using the z score table.
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