How to Calculate a Z-Score

A z-score is used in statistics to express how many standard deviations away a number is from the mean. Find out how to calculate your z-score with these steps.

Instructions

  • Step 1: Find that the total is two. Your z-score is 2, since 130 is exactly 2 standard deviations above the mean of 100. Now impress your friends by telling them your z-score!
  • FACT: The 68-95-99.7 statistics rule states that about 68 percent of values in a normal distribution lie within 1 standard deviation of the mean; 95 percent of the values lie within 2; and 99.7 percent of the values lie within 3 standard deviations of the mean.
  • Step 2: Take the score of 130 and subtract the mean, which is 100, for a sum of 30. Divide this by the standard deviation, which is 15.
  • TIP: Standard deviation measures how much, on average, individual scores of a given group deviate from the average, or mean, score of the group.
  • Step 3: Determine the mean and deviation. If the test is an IQ test, for example, it would have a mean of 100 and a standard deviation of 15.
  • Step 4: Start with the score itself. For example, say you've scored 130 on a standardized test, and you want to find the z-score. The score would be 130.

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