This means that the data point is significantly different from the mean at a 95% confidence level. Furthermore, the magnitude of the z-score quantifies the distance between the data point and the mean in terms of standard deviations.Ī: A z-score of +/- 1.96 or greater is considered statistically significant at the 5% level of significance (i.e., p < 0.05). When the z-score is positive, it signifies that the data point lies above the mean, and when the z-score is negative, it denotes that the data point is below the mean. By standardizing the data, we can make meaningful comparisons and identify outliers and extreme values.Ī: A z-score of 0 indicates that the data point corresponds to the mean.
The z-score is obtained by taking the difference between the data point and the mean, and dividing it by the standard deviation.Ī: Z-scores are useful because they allow us to compare data points from different datasets that have different scales and units of measurement. George did better than 150 students.Ī: A z-score is a statistical measure that tells us how many standard deviations a data point is from the mean of a dataset. This means that almost 75% of the students scored lower than George and only 25% scored higher. Multiply this number by 100 to get percentages. Then go to the x axis to find the second decimal number (0.07 in this case). Find the first two digits on the y axis (0.6 in our example). For George’s example we need to use the 2nd table as his test result corresponds to a positive z-score of 0.67.įinding a corresponding probability is fairly easy.
If a z-score calculation yields a negative standardized score refer to the 1st table, when positive used the 2nd table. If you noticed there are two z-tables with negative and positive values. standard normal distribution table) comes handy. Now, in order to figure out how well George did on the test we need to determine the percentage of his peers who go higher and lower scores.
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