Question

Why would there be a difference between percentages with the Empirical Rule and the actual percentages?

Answer 1

Answer:

Given that $\int\limits^a_b {\frac{1}{2\pi } e^{-1/2} x} \, dx$   is not the easiest equation to solve, and that

the values at the convenient ± 1 sigma,± 2 sigma,± 3 sigma are irrational

using the "rule-of-thumb" "empirical rule" is typically "close enough"

given that the whole probability analysis by definition has some uncertainty in it

Step-by-step explanation:

Answer 2

The percentages of a normal distribution data lies within three standard deviations of its mean for empirical rule while it's definite for actual percentages.

What is the empirical rule?

The empirical rule is also referred to as the 68-95-99.7 rule and it can be defined as a rule in statistics which states that:

• The middle 68% of a normal distribution would be within one standard deviation of its mean (µ ± σ).

• The middle 95% of a normal distribution would be within two standard deviations of its mean (µ ± 2σ).

• The middle 99.7% of a normal distribution would be within three standard deviations of its mean (µ ± 3σ).

In Statistics, there is a difference between percentages calculated by using the empirical rule and the actual percentages because a normal distribution data lies within three standard deviations of its mean for the former but it is definite for the latter.

In conclusion, the empirical rule is more important to researchers and statistician because it can be used to determine outcomes and gain insight even when all the data aren't available.

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