What is a "Z-Score," and what is it used for?
What does a Z-Score do?
Z-Scores tell us whether a particular score is equal to the mean, below the mean or above the mean of a bunch of scores. They can also tell us how far a particular score is away from the mean. Is a particular score close to the mean or far away?
Z-Scores help us to compare individual scores from different bunches of data. We can use Z-scores to standardize scores from different groups of data. Then we can compare raw scores from different bunches of data. To use standardised weighted add as an example, it means that the each students marks are compared to the average. A student who performed well in a "difficult" (low average mark) task will have a greater weighting that a student who did well in an "easy" (high average mark) task. It also helps to remove "statistical anomalies" when creating an estimate.
If a Z-Score...
- Has a value of 0, it is equal to the group mean.
- Is positive, it is above the group mean.
- Is negative, it is below the group mean.
- Is equal to +1, it is 1 Standard Deviation above the mean.
- Is equal to +2, it is 2 Standard Deviations above the mean.
- Is equal to -1, it is 1 Standard Deviation below the mean.
- Is equal to -2, it is 2 Standard Deviations below the mean.