A z-score is a standard statistic used to compare two numbers from different normal distributions. We use it to normalize judge scores, when judges are evaluating different groups of competitors.

Here's an example to illustrate this, using Judge Smith.

**Step 1: Judge Smith completes her scores**

Judge Smith evaluates 10 competitors, generating 10 scores (one for each competitor).

**Step 2: Calculate average and standard deviation for Judge Smith**

Our first step is to calculate the average and standard deviation of those 10 scores.

**Step 3: Calculate the z-scores, one for each competitor**

At this point, we have three numbers for each competitor- the competitor's score (*x*), the average score from Judge Smith (μ), and the standard deviation (σ) from Judge Smith. We use the three of these numbers to generate the z-score (Z).

We repeat this math for each competitor that Judge Smith looks at. Each competitor gets their own z-score from Judge Smith, and Judge Smith has 10 z-scores.

Essentially, the z-score is a measurement of how far (how many standard deviations) her score is from the average.

**Step 4: Average the z-scores**

If a competitor is evaluated by more than one judge (Judge Smith, Judge Judy, and Judge Conti, let's say), that competitor will have three z-scores, one from each judge.

We then average those z-scores to get the average z-score for that one competitor.