![]() Z-scores are useful because they give us an idea of how an individual value compares to the rest of a distribution.įor example, is an exam score of 87 good? Well, that depends on the mean and standard deviation of all exam scores. ![]() This tells us that an exam score of 80 is exactly equal to the mean. The individual value we’re interested in is X = 80.Question 3: Find the z-score for an exam score of 80. This tells us that an exam score of 75 lies 1.25 standard deviations below the mean. The individual value we’re interested in is X = 75.Question 2: Find the z-score for an exam score of 75. This tells us that an exam score of 87 lies 1.75 standard deviations above the mean. The individual value we’re interested in is X = 87.We can use the following steps to calculate the z-score: Question 1: Find the z-score for an exam score of 87. Suppose the scores for a certain exam are normally distributed with a mean of 80 and a standard deviation of 4. Example: Calculate and Interpret Z-Scores The following example shows how to calculate and interpret z-scores. The larger the absolute value of the z-score, the further away an individual value lies from the mean. A z-score of 0: The individual value is equal to the mean.Negative z-score: The individual value is less than the mean.Positive z-score: The individual value is greater than the mean.We use the following formula to calculate a z-score:Ī z-score for an individual value can be interpreted as follows: This means that for a normally distributed population, there is a 36.864% chance, a data point will have a z-score between 0 and 1.12.īecause there are various z-tables, it is important to pay attention to the given z-table to know what area is being referenced.In statistics, a z-score tells us how many standard deviations away a given value lies from the mean. each value in the table is the area between z = 0 and the z-score of the given value, which represents the probability that a data point will lie within the referenced region in the standard normal distribution.įor example, referencing the right-tail z-table above, a data point with a z-score of 1.12 corresponds to an area of 0.36864 (row 13, column 4).the row headings define the z-score to the tenth's place.the column headings define the z-score to the hundredth's place.The values in the table below represent the area between z = 0 and the given z-score. There are a few different types of z-tables. A positive z-value indicates that the point lies to the right of the mean, and a negative z-value indicates that the point lies left of the mean. On the graph of the standard normal distribution, z = 0 is therefore the center of the curve. A z-score of 0 indicates that the given point is identical to the mean. Z-tableĪ z-table, also known as a standard normal table or unit normal table, is a table that consists of standardized values that are used to determine the probability that a given statistic is below, above, or between the standard normal distribution. The z-score has numerous applications and can be used to perform a z-test, calculate prediction intervals, process control applications, comparison of scores on different scales, and more. For a sample, the formula is similar, except that the sample mean and population standard deviation are used instead of the population mean and population standard deviation. Where x is the raw score, μ is the population mean, and σ is the population standard deviation. The z-score can be calculated by subtracting the population mean from the raw score, or data point in question (a test score, height, age, etc.), then dividing the difference by the population standard deviation: z = Values above the mean have positive z-scores, while values below the mean have negative z-scores. The z-score, also referred to as standard score, z-value, and normal score, among other things, is a dimensionless quantity that is used to indicate the signed, fractional, number of standard deviations by which an event is above the mean value being measured. Use this calculator to find the probability (area P in the diagram) between two z-scores. This is the equivalent of referencing a z-table. Please provide any one value to convert between z-score and probability. Use this calculator to compute the z-score of a normal distribution. Home / math / z-score calculator Z-score Calculator
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