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A z score, or standard score, indicates how many standard deviations an element is from the mean of a dataset. It is calculated using the formula: z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. A z score can help determine the relative position of a value within a distribution, allowing for comparisons across different datasets.

The mean is the average of a set of values, calculated by summing all values and dividing by the number of values. The standard deviation measures the amount of variation or dispersion in a set of values; a low standard deviation indicates that values tend to be close to the mean, while a high standard deviation indicates a wider spread. Together, these statistics provide a summary of the data's central tendency and variability.

In statistics, significance often refers to whether a result is likely due to chance or if it reflects a true effect. A z score can help assess significance by indicating how extreme a value is within a distribution. Typically, a z score beyond ±1.96 is considered significant at the 0.05 level, suggesting that the observed value is unlikely to occur under the null hypothesis, thus indicating a potential anomaly or noteworthy observation.