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Z-score definition

Most of us understand Z-score, but it's nice to get a refresher.
  1. Define - Define the term Z-score.
  2. Context - Use Z-score in a sentence.
  3. Quiz - Test your knowledge.
by Paul Alan Davis, CFA, July 16, 2016
Updated: January 4, 2019
Despite the fairly strict assumptions that come with the Z-score, it remains a popular place to start with distributions due to its simplicity.

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Z-score

Intermediate

Z-score is a statistical term showing the number of standard deviations above or below the mean the data point sits, relative to the set of data being tested.

Mathematically it 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.

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

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 to say Z-score .

Video

Many terms have 4-5 minute videos showing a derivation and explanation. If this term had one, it would appear here.

Videos can also be accessed from the YouTube Channel.

Video Script

If this term had a video, the script would be here.

Quiz

Click box for answer.

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

Questions or Comments?

Still unclear on the term Z-score? Try out the course Quant 101.

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