A Z-Score Table is a table that shows the percentage of values (or area percentage) to the left of a given z-score on a standard normal distribution.Ī positive Z-score means that the observed value is above the mean of total values.Ī negative Z-score value indicates the observed value is below the mean of total values. To find a specific area under a normal curve, first, find the z-score of the data value and then use a Z-Score Table to find the area. This z-score will tell you how many standard errors are there between the sample mean and the population means. Standard Error of the Mean: When you have multiple samples and want to describe the standard deviation of those sample means (the standard error) use this z score formula: Putting the values in the equation mentioned above, Solution From the question above we can deduce that,Īnd the value of standard deviation (σ) is 30 Assuming it is a normal distribution, your z score would be. The test has a mean (μ) of 140 and a standard deviation (σ) of 30. Let's take an example and understand this better. Where x̄ is the sample means is the sample standard deviation. How to Calculate Z-score?įor a sample, the basic z- score formula is When you 'standardize' a variable, its mean becomes zero and its standard deviation becomes one. Z-scores range from -3 standard deviations up to +3 standards.Ī Z-score can help us in determining the difference or the distance between a value and the mean value.

A raw score as a Z-score can also be called a standard score and it can be placed on a normal distribution curve. A data point is a measure of how many standard deviations are below or above the mean. Z-score can be defined as the number of standard deviations from the mean.

Standard normal curve z score table