Calculate the Z-Score for a given raw score, population mean, and standard deviation, and visualize the Z-score on a standard normal distribution curve.
Z score: (X - π) / π =
Understanding the Z-Score
The Z-score, also known as the standard score, tells us how many standard deviations a data point (or raw score) is from the mean of the population. A Z-score can be either positive or negative, depending on whether the raw score is above or below the mean.
Formula for Calculating the Z-Score
The formula for calculating the Z-score is:
Where:
- X: The raw score (the value you are analyzing).
- ΞΌ (mu): The mean of the population.
- Ο (sigma): The standard deviation of the population.
Interpreting the Z-Score
A Z-score of 0 means the raw score is exactly equal to the mean. Positive Z-scores indicate the raw score is above the mean, while negative Z-scores indicate it is below the mean.
- Z = 0: The raw score is exactly equal to the population mean.
- Z = 1: The raw score is 1 standard deviation above the mean.
- Z = -1: The raw score is 1 standard deviation below the mean.
- Z = 2: The raw score is 2 standard deviations above the mean, and so on.
Visualizing the Z-Score
In the visualization above, we plot a standard normal distribution, which has a mean of 0 and a standard deviation of 1. The Z-score you calculate will be plotted on this curve, and the shaded area represents the probability (or proportion of the data) that lies to the left of your Z-score.
This visualization helps you understand how unusual or common your Z-score is in relation to the standard normal distribution.
Further Reading
Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, heβs focused on bringing more fun and curiosity to the world of science and research online.