Z = (X - μ) / σ

In this equation:

Z denotes the Z-score

X refers to the value of the data point

μ represents the mean of the distribution

σ stands for the standard deviation of the distribution

Identifying Outliers: The utilization of Z-scores proves instrumental in uncovering potential outliers in a dataset. Data points linked to Z-scores that noticeably deviate from the mean (either greater than +3 or less than -3) could be flagged as outliers, necessitating further scrutiny.

Calculating Percentiles: Z-scores play an active role in the calculation of percentiles. These percentiles delineate the relative standing of a data point within a distribution. With the aid of a Z-score table or calculator, determining the percentile rank of a data point becomes feasible.

Assumption of Normality: Z-scores operate under the presumption that data adheres to a normal distribution. If the underlying distribution deviates from normality, Z-scores might not accurately portray the data's relative position within the distribution.

Influence of Extreme Values: In distributions plagued with extreme values or outliers, the mean and standard deviation could be skewed. This distortion might lead to Z-scores that provide potentially deceptive information.

The Atlanta Falcons career touchdown leaders represent the players who have scored the highest number of touchdowns throughout their tenure with the team.

All topics#### Popular topics

The Iraq War, initiated in 2003 by a US-led coalition, was a controversial military campaign that aimed to dismantle the regime of Saddam Hussein, causing significant casualties and humanitarian concerns. Read more »