Z Score Calculator

A z-score can be defined as how many standard deviations away a value X from the mean. If a value is exactly an average, z-score will be 0. Values above the mean have positive z-scores whereas values below the mean have negative z-scores.

The Z score is computed as:

$$ Z = \frac{(X-\mu)}{\sigma} $$

Here μ is the Population mean and σ is the population standard deviation. X is called as raw score.


$$ Z = \frac{(X-\mu)}{\sigma} $$

Assumptions of Z Score

  1. Normal Distribution: Z score assumes that the data is normally distributed.
  2. Independence: Z score assumes that the data points are independent of each other. If the data points are not independent, the Z-score may not accurately show the variation within the data.
  3. Sample Size: The sample size must be sufficiently large to provide a representative sample of the population.
  4. Continuous Data: The data must be measured on a continuous scale. If the data is measured on a categorical or ordinal scale, the Z-score may not be appropriate.
  5. Outliers: The Z-score assumes that the data does not contain outliers or extreme values.

Examples of Z Score

Example 1: Suppose a student scored 75 on a test with a mean of 65 and a standard deviation of 5. The Z-score for this student would be:

Z = (75 - 65) / 5 = 2

Example 2: Suppose the heights of a group of people are normally distributed with a mean of 68 inches and a standard deviation of 3 inches. A person who is 71 inches tall would have a Z-score of:

Z = (71 - 68) / 3 = 1

Example 3: Suppose a company's sales are normally distributed with a mean of $50,000 and a standard deviation of $10,000. If the company had sales of $75,000 in a given month, the Z-score for that month's sales would be:

Z = (75,000 - 50,000) / 10,000 = 2.5

ListenData Logo
Spread the Word!
Looks like you are using an ad blocker!

To continue reading you need to turnoff adblocker and refresh the page. We rely on advertising to help fund our site. Please whitelist us if you enjoy our content.