A PHP Error was encountered

Severity: Warning

Message: count(): Parameter must be an array or an object that implements Countable

Filename: controllers/formulas.php

Line Number: 37

Empirical Rule Formula Online - Tutorpace

Empirical Rule Formula

Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.


Definition:-The empirical rule is an important rule of thumb that is used to state the approximate percentage of values that lie within a given number of standard deviations from the mean of a set of data if the data are normally distributed.
The empirical rule is used only for three numbers of standard deviations 1σ,2σ, and 3σ.

Distance from the mean Values within Distance
µ±1σ 68%
µ±2σ 95%
µ±3σ 99.7%

If a set of data is normally distributed, or bell shaped
·         approximately 68% of the data values are within one standard deviation of the mean
·         95% are within two standard deviations, and
·         Almost 100% are within three standard deviation.

Example:-   Support a recent report states that for California, the average statewide price of a gallon of regular gasoline was $1.42. Suppose regular gasoline price varied across the state with a standard deviation of $0.08 and were normally distributed.

According to empirical rule,
Approximately 68% of the prices should fall within
µ±1σ= 1.42 ±1*0.08
         = (1.42- 0.08, 1.42+0.08)
          = (1.34, 1.5)

Similarly 95% of the prices should fall within
µ±2σ= 1.42 ±2*0.08
         = (1.42- 0.16, 1.42+0.16)
          = (1.26, 1.58)

And 99.7% of the prices should fall within
µ±3σ= 1.42 ±3*0.08
         = (1.42- 0.24, 1.42+0.24)
          = (1.18, 1.66)


HAVE A QUESTION? Chat With Our Tutoring Experts Now