As a statistical expert with a deep understanding of data analysis and interpretation, I can provide a comprehensive explanation of what it means to have a negative z-score.
When you calculate a z-score for a data point, you're essentially measuring how many standard deviations away from the mean that data point lies. The mean, or average, is a central value in a data set that represents the typical value for the group. The standard deviation is a measure of how much variation there is from the mean. It tells you how spread out the numbers are in the data set.
A negative z-score indicates that the data point is below the mean. This means that the value is lower than the average value of the group. The magnitude of the z-score tells you how far away from the mean the data point is. The larger the absolute value of the z-score, the further away the data point is from the mean.
For example, if a data point has a z-score of -2, this means that the data point is two standard deviations below the mean. This suggests that the value is relatively low compared to the other values in the data set. Conversely, if a data point has a z-score of +2, it is two standard deviations above the mean, indicating that it is relatively high compared to the other values.
It's important to note that z-scores are unitless, which means they are not tied to any specific unit of measurement. This makes them very useful for comparing data across different variables and units. For instance, you could use z-scores to compare a student's height to their weight, even though height is measured in inches or centimeters and weight is measured in pounds or kilograms.
In addition to identifying where a data point lies relative to the mean, z-scores can also be used to identify outliers. Outliers are values that are significantly different from the rest of the data. A common rule of thumb is that any data point with a z-score greater than +3 or less than -3 is considered an outlier. This is because data points that are more than three standard deviations away from the mean are relatively rare and may indicate an error in data collection or an unusual event.
Z-scores are also used in hypothesis testing, which is a statistical method used to determine whether there is a significant difference between two groups or a relationship between two variables. In this context, a z-score is calculated for the test statistic, and the resulting value is compared to a critical value to determine whether to reject the null hypothesis.
In summary, a negative z-score indicates that a data point is below the mean of a data set, and the magnitude of the z-score tells you how many standard deviations away from the mean the data point is. Z-scores are a valuable tool for data analysis because they allow you to compare data across different variables and units, identify outliers, and conduct hypothesis testing.

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Z-scores may also be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean. Positive and negative scores also reveal the number of standard deviations that the score is either above or below the mean.read more >>