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# Z-Score Definition, Excel Example and Quiz

Most of us understand Z-Score, but it's nice to get a refresher.
1. Define - Learn about the term Z-Score for Finance.
2. Context - Use Z-Score in a sentence.
3. Quiz - Test yourself. by Paul Alan Davis, CFA
Updated: February 18, 2021
Despite the fairly strict assumptions that come with the Z-Score, it remains a popular place to start discussions of distributions due to its ease of interpretation.

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## Interpreting Z-Score for Finance and Investments

Intermediate

Z-Score is a statistical term showing the number of standard deviations above or below the mean a data point sits. This encompasses the distribution of the data set being measured and technically is for population data, whereas the t-statistic is reserved for samples.

Synonyms: standard score, standardize, z-value, normal score, standardized value

Mathematically Z-Score is the raw data point (observation) minus the mean, then divided by the standard devation.

• Z-score = (Raw Score - Mean) / Standard Deviation

The Z-score is typically used when the population mean and standard deviations are known. Because this isn't usually practical, sample measures are used when sample sizes are large.

In cases where sample sizes are small then the Student's t-statistic is preferred.

For context, in the investment space, because the full population of investments is too difficult or costly to survey, samples are used and, in practice the Z-Score provides estimates that are very close to those from the t-distribution, so many practioners use the Z-Score for its simplicity and availability in statistical analysis software packages.

The `=STANDARDIZE()` function in Excel is used to find a normalized value from a distribution characterized by a mean and standard deviation. It takes three inputs, the raw score, the mean and the standard deviation.

For example, a stock with an observed return value (raw score) of 10% when its mean was 7% and standard deviation was 15%, would translate to a Z-Score of 0.20. This could then be translated into a probability assessment or aid in hypothesis testing.

### In a Sentence

Sam:  If the Zed-score requires a known population, why is it so common in Finance?
Leo:  To translate. I think our friend from Canada meant Z-Score.

### Video

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### Video Script

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### Quiz

The Z-score is useful for estimation when sample sizes are small and if the population standard deviation is known. | True or False?

False. The first part is false and the second is true.

A Z-score can be positive or negative. | True or False?

True

Still unclear on the term Z-score? Try out the course Quant 101 with 27 free videos on financial modeling in Excel.

### Related Terms

Our trained humans found other terms in the category statistical distributions you may find helpful.

## What's Next?

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