Raw score: 68. First we need to find the z-score. Notice that the z-score is negative. The raw score is below the mean. Due to the fact that we have a negative z-score, we will need to use a z score table that has negative values. A score of 68 only has 6.81% of scores below it and 93.19% of scores are higher than it. A z-score of 1.5, then, means that a value is 1.5 standard deviations greater than the mean. Z-scores can be negative if they are below the mean, so for the three-sigma rule, 68% of the values fall between the z-scores of -1 and 1. In other words, if a z-score is 1.5, it is 1.5 standard deviations away from the mean. The z-score. The number of standard deviations from the mean is called the z-score and can be found by the formula. z = x − m σ. Example 1. Find the z-score corresponding to a raw score of 132 from a normal distribution with mean 100 and standard deviation 15. Solution. It can be used to compare different data sets with different means and standard deviations. It is a universal comparer for normal distribution in statistics. Z score shows how far away a single data point is from the mean relatively. Lower z-score means closer to the meanwhile higher means more far away. Positive means to the right of the mean Negative z-scores correspond to raw scores that lie below the mean while positive z-scores correspond to raw scores that lie above the mean. The p-value is the probability that the mean is higher than or equal to a specific score. P-values can be converted to percentages: p-value = 0.95 x 100 = 95 percent. A z-score is measured in units of the standard deviation. For example, if the mean of a normal distribution is five and the standard deviation is two, the value 11 is three standard deviations above (or to the right of) the mean. The calculation is as follows: x = μ + (z)(σ) = 5 + (3)(2) = 11. The z-score is three. The mean for the standard A z-score is an example of a standardized score. A z-score measures how many standard deviations a data point is from the mean in a distribution. Questions Tips & Thanks Want to join the conversation? Sort by: Top Voted Ryan Giglio 5 years ago When I paused to calculate the standard deviation myself, I came up with 1.83, not 1.69. A z z -score is a standardized version of a raw score ( x x) that gives information about the rel ative location of that score within its distribution. The formula for converting a raw score into a z z -score is: z = x − μ σ (5.2.1) (5.2.1) z = x − μ σ. for values from a population and for values from a sample: They are .5 standard deviations above the mean in English: Z = (45-40)/10 = .5. Their Z-score in statistics is Z = (38-30)/5 = 1.6. Note that we can compare all these scores against each other only once converted to Z-scores. In statistics, if a student had a score of 40, that would be a very good grade! Z-Score Table. A z-table, also known as the standard normal table, provides the area under the curve to the left of a z-score. This area represents the probability that z-values will fall within a region of the standard normal distribution. Use a z-table to find probabilities corresponding to ranges of z-scores and to find p-values for z-tests. iMaaA.