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Z-Scores! Uh, no. Z-Scores! Uh, no we don't just have an accent when we're saying it.

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It really is Z-Scores. All right, so, let's get to zhe problem.

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What are Z-Scores, and where does the catchy name come from?

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The Z in Z-Scores refers to the Z distribution,

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another name for the normal distribution. Distant cousin of the...

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weird distribution. That's because Z-Scores tell us how many standard deviations...

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a data point is above or below an average, when placed on a...

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standard normal curve, or a curve with a mean zero and standard deviation of one. It looks like...

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this. What's useful about these Z-Scores is that we can use our handy-dandy...

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probability Z-Score chart to find the probability under the curve of any specific data point.

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And this is super useful, because we can find the likelihood of a specific data point occurring, just by...

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knowing its Z-Score. But the data we're given sometimes doesn't come from a standard normal distribution,

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which means we have to standardize our data first before we can use our chart. Now here's a formula to...

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help us standardize our data. Z equals the point we're interested in. X - μ,

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the mean, all over the standard deviation. This squiggly line thing here is standard deviation.

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Suppose we had a patient take a reading abilities test.

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The patient scores a 46 on the test, and the mean of the test scores is 52. With a standard...

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deviation of four. Got it? Well, we want to find the percentile of the...

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patient's score. First, we have to standardize the data, and we'd use our little handy-dandy formula...

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and plug in some numbers. We get Z equals 46 minus 52 over 4, which is negative...

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six over four, which is negative three halves, or negative 1.5. A negative...

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Z-Score means our point is left of, or smaller than,

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the mean, while a positive Z-Score means our...

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number is to the right of, or larger than, the mean.

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Well, yeah, we already knew that when we were told that...

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our point was 46 and our mean was 52.

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We figured that out okay. Our Z-Score is negative 1.5, so we can look at our chart, and we see that our...

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percentage is 0.0668, or the 6.68th percentile.

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