Since \(x = 17\) and \(y = 4\) are each two standard deviations to the right of their means, they represent the same, standardized weight gain relative to their means. Z scores above the mean are positive and Z scores below the mean are negative. The mean of the standard normal distribution is 0.
A negative weight gain would be a weight loss. A Z score represents how many standard deviations an observation is away from the mean. To understand the concept, suppose \(X \sim N(5, 6)\) represents weight gains for one group of people who are trying to gain weight in a six week period and \(Y \sim N(2, 1)\) measures the same weight gain for a second group of people. The z-score allows us to compare data that are scaled differently. Therefore, \(x = 17\) and \(y = 4\) are both two (of their own) standard deviations to the right of their respective means.
This means that four is \(z = 2\) standard deviations to the right of the mean.
Or you can use the Online Percentage Calculator.= 2 \nonumber\] Multiply resultant value by 100 to get a percentage score. 0 z Cumulative probabilities for POSITIVE z-values are in the following table. 3) Join the X and Y axisĪs a result, we get 0.71566 4) Convert resultant value into percentage The second step is to look at the second decimal number on X-axis. Now we have to find out the corresponding probability from the table. What is a good z-score There isn't a definite good or bad z-score. It can be used to describe the distance of a value from the mean in terms of standard deviations. In John's case, we will use the positive table because we get a positive z-score of 0.57. A z-score is a statistical measure that quantifies how many standard deviations a data point is away from the mean of the dataset. Similarly, if we get a negative z-score, then we will use the negative table. Examine the table and note that a 'Z' score of 0.0 lists a probability of 0.50 or 50, and a 'Z' score of 1, meaning one standard deviation above the mean, lists a probability of 0.8413 or 84. If we get a z-score positive then we will use a positive table. The table in the frame below shows the probabilities for the standard normal distribution. So, keep it handy.Īs we all know that there are two z-tables with positive and negative values. For that, we will use a Z-Table (or Standard Normal Distribution Table). To check how well John performed, we need to find the percentage of highest and lowest scores of other students.
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