What is a z-score?
A z-score measures the distance, or how many standard deviations, a data point is from the mean. A z-score of 2 means your data point is 2 standard deviations above the mean. A z-score of 0 means your data point is the mean, and a z-score of -2 means your data point is 2 scores below the mean.
What is the formula?
- z= (x-µ)/𝜎
- Where z is the z- score
- X is your data point
- µ is the mean
- 𝜎 is the standard deviation
What are z-scores used for?
- z-scores can be used to compare two different data values on two different scales
- z-scores can also be used to find what percent of the the data lies above and below your data values
- z-scores are also used in some hypothesis tests
You took the sat and your best friend took the act. You scored a 780 on the sat and your friend scored a 12 on the act. The average for the sat scores this year was a 1500 with a standard deviation of 250. And the average for the act scores this year was 20.8 with a standard deviation of 4.8.
Therefore, your friend did better than you did.