Empirical Rule Formula

About Empirical Rule Formula

The empirical rule formula (also known as the 68 95 99 rule formula) uses normal distribution data to determine how far the first, second, and third standard deviations depart from the mean value by 68, 95, and 99 percent, respectively. It also shows that all of the data (99%) falls inside the third standard deviation band (either above or below the mean value). The empirical rule formula is described here, along with examples that have been solved. More Maths Formulas on the parent's page.

What is the Empirical Rule Formula?

The empirical rule formula is used to compute the first, second, and third standard deviations, as well as the percentage likelihood that the data will fall within that range. The empirical rule formula for a particular sequence is as follows:

first standard deviation = µ - σ to µ + σ (68% data)

second standard deviation = µ - 2σ to µ + 2σ (95% data)

third standard deviation = µ - 3σ to µ + 3σ (99% data)

Where, µ = mean and σ = standard deviation

Solved Example of Empirical Rule Formula

Example: People that enter a store are regularly distributed, with a mean of 25 and a standard deviation of 3. The percentage possibility of individuals coming at the store is 19 to 31.

  1. Sol: To find the percentage chance of 19 to 31 people at the store
  2. Given: µ = 25 and σ = 3
  3. Now, by using the Empirical rule formula, first standard deviation = µ - σ to µ + σ
  4. = (25-3) to (25+3)
  5. = 22 to 28
  6. second standard deviation = µ - 2σ to µ + 2σ
  7. = (25 - 2 × 3) to (25 + 2 × 3)
  8. = (25 - 6) to (25 + 6)
  9. = 19 to 31
  10. chances of 20 people arriving at the store are 95%

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Empirical Rule Formula

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