Z Scores

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When you want to compare different types of data you have to standardize it. When you standardize a data set, you change the scale to a neutral scale so that you can compare it to other types of data.


 * For example, say you want to compare your Biology test grade to your friend's Trigonometry test grade. Since they aren't the same tests (one might have been harder than the other) you have to transform your grades into a neutral scale (standardize them). This will allow you to compare grades to see who really did better!

The most common method of standardizing a data set is by using z scores. The z score states how far a score falls from the mean in standard deviation units. It does this by transforming a distribution into one that has a mean of zero and a standard deviation of 1. That way, the probability of being a given standard deviation away from the mean is the same for all distributions. This is possible because the z distribution is based on the normal curve.

Once you calculate your z score, you can tell how far it falls from the mean, what percentage of scores fall below/above your score, and what percentage of scores fall between the mean and your score.

Calculating a z score isn't too bad either! All you need to know is the score, the mean, and the standard deviation. In most cases, you'll only use the formula for calculating z scores in a sample. Using the population formula is highly unlikely unless you are working with IQ or some other rare known population parameter.