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Let's see how that works. A quick peek at some of our scores on our first IQ test shows a minimum of 1 and a maximum of 6. However, we'll gain much more insight into these scores by inspecting their histogram as shown below. The histogram confirms that scores range from 1 through 6 and each of these scores occurs about equally frequently.

This pattern is known as a uniform distribution and we typically see this when we roll a die a lot of times: numbers 1 through 6 are equally likely to come up. Note that these scores are clearly not normally distributed. We suggested earlier on that giving scores a common standard of zero mean and unity standard deviation facilitates their interpretation.

We can do just that by. By entering these numbers into the formula, we see why a score of 5 corresponds to a z-score of 0. In practice, we obviously have some software compute z-scores for us. We did so and ran a histogram on our z-scores, which is shown below. If you look closely, you'll notice that the z-scores indeed have a mean of zero and a standard deviation of 1.

McLeod, S. Z-score: definition, calculation and interpretation. Simply Psychology. Toggle navigation. Saul McLeod , published What does the z-score tell you?

The SND i. For example, if the distribution of raw scores if normally distributed, so is the distribution of z-scores. Therefore, one standard deviation of the raw score whatever raw value this is converts into 1 z-score unit. Download this article as a PDF. Further Information. How to reference this article: How to reference this article: McLeod, S. Back to top. What does the z-score tell you? Why are z-scores important?

How do you calculate the z-score? Develop and improve products. List of Partners vendors. Your Money. Personal Finance. Your Practice.

Popular Courses. Table of Contents Expand. Standard Deviation. The Bottom Line. Z-Score and Standard Deviation: An Overview Although the finance industry can be complex, an understanding of the calculation and interpretation of fundamental mathematical building blocks is still the foundation for success, whether in accounting, economics, or investing.

Key Takeaways Standard deviation defines the line along which a particular data point lies. Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean.

Bollinger Bands are a technical indicator used by traders and analysts to assess market volatility based on standard deviation. Article Sources. Investopedia requires writers to use primary sources to support their work. These include white papers, government data, original reporting, and interviews with industry experts. We also reference original research from other reputable publishers where appropriate. You can learn more about the standards we follow in producing accurate, unbiased content in our editorial policy.

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Related Articles. Partner Links. A bell curve describes the shape of data conforming to a normal distribution. It is set a specified number of standard deviations from the mid-point. What Is a Z-Test?