The Z-score is a statistical measure that represents the number of standard deviations a data point is from the mean of a dataset. It is used to identify outliers in the data and to assess the statistical significance of results. To calculate the Z-score, you need to know the mean and standard deviation of the dataset. Here is the formula for calculating the Z-score:
Z-score = (X – Mean) / Standard Deviation
Where X is the value of the data point, Mean is the mean of the dataset, and Standard Deviation is the standard deviation of the dataset.
For example, let’s say you have a dataset with a mean of 100 and a standard deviation of 10, and you want to calculate the Z-score for a data point with a value of 120. The Z-score would be calculated as follows:
Z-score = (120 – 100) / 10 = 2
This means that the data point with a value of 120 is 2 standard deviations above the mean of the dataset.
The Z-score can be used to identify outliers in the data by setting a threshold for the number of standard deviations a data point must be above or below the mean to be considered an outlier. For example, a data point with a Z-score of 3 or greater might be considered an outlier. The Z-score can also be used to assess the statistical significance of results by comparing the Z-score to a critical value from a standard normal distribution table. If the Z-score is greater than the critical value, the result is statistically significant.
