Definition of Z Score
Z score or standard score describes a value's relationship to the mean of a group of values. It is a measure of how far the data point is from the mean. Technically, it is the number of standard deviations below (indicated in negative) or above (indicated in positive) the population mean.
How is it Calculated?
The formula is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
The process of conversion of the raw sore into a standard score through standardisation or normalisation. The standard scores are most commonly called Z Scores.
The Z Score is usually placed on a normal distribution curve and its range is -3 and +3 standard deviations. It is essential to know the mean and the population standard deviation in order to arrive at and plot this figure.
How Can It Be Used in Real Life?
- It can be used to determine various real world probabilities such as IQ score, insect length, heights of females, or SAT scores, provided one knows the mean and standard deviation.
- Z scores, in finance, help the traders determine the market’s volatility. This measure is also known as Altman Z score.
- It can be used to determine the overall financial health of the company. helps gauge the likelihood of bankruptcy for a publicly traded company. The Z-score is based on five key financial ratios found in the company’s annual reports.
- In educational assessment, the T-score is a standard score Z shifted. The T score is scaled to have a mean of 50 and a standard deviation of 10.
Criticism of Z Scores
- It is not immune to false accounting practices.
- It isn’t effective for new companies that have little or no earnings.
- It does not address cash flows of the company.
- Z scores can swing from quarter to quarter if a company records one time write-offs and the scores might indicate false bankruptcy.
