Easily calculate the standard score (Z-score) for any raw data point. Understand statistical significance and probability distributions in seconds.
This score indicates that your raw data point is 0 standard deviations above/below the population mean.
In statistics, a Z-score (also known as a standard score) describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean.
The Z-score tells you exactly how many standard deviations a specific data point is away from the mean. If a Z-score is 0, it means the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean. Z-scores may 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.
The formula for calculating a Z-score is relatively simple:
z = (x - μ) / σ
z = Z-score
x = The value being evaluated (Raw Score)
μ = The Mean of the population
σ = The Standard Deviation of the population
Let's say you take a test and score 85. The class average (mean) was 70, and the standard deviation was 10.
To find the Z-score:
z = (85 - 70) / 10
z = 15 / 10
z = 1.5
This means your score is 1.5 standard deviations above the average. This is a very good result!
Generally, a Z-score close to 0 indicates the value is near the average. Positive scores are above average, and negative scores are below. In standard testing, scores above +2.0 or below -2.0 are often considered "outliers" or statistically significant anomalies.
Yes! A negative Z-score simply means the data point is below the mean (average). For example, if the average height is 5'9" and you are 5'5", you would have a negative height Z-score.
They allow you to compare scores from different datasets that have different means and standard deviations. It standardizes the data onto a common scale.
