Empirical Rule
You are currently viewing a sample of the Cram Kit. Click here to unlock everything.
The Empirical Rule states that in a normal distribution...
- 68% of data points fall within 1 standard deviation of the mean
- 95% of data points fall within 2 standard deviations of the mean
- 99.7% of data points fall within 3 standard deviations of the mean
Scenario: Consider the distribution of IQ scores, which is normal and has a mean (µ) of 100 and a standard deviation (σ) of 15.
68% of IQ scores are contained within +/- 1σ of the mean (µ).
95% of IQ scores are contained within +/- 2σ of the mean (µ).
99.7% of IQ scores are contained within +/- 3σ of the mean (µ).
A Use Case for the Empirical Rule
Scenario: You have an IQ score of 115. Considering that IQ scores lie on a normal distribution with a mean (µ) of 100 and a standard deviation (σ) of 15, what percentage of the US Population are you smarter than?
| Clue | Insight |
|---|---|
| "What percentage of the US Population are you smarter than?" essentially means what percent of IQ scores fall below ours of 115? | We'll use the Empirical Rule to determine the space under the curve to the left of our IQ. |
x = 115
µ = 100
σ = 15
σ away from µ = (x - µ) / σ
σ away from µ = (115 - 100) / 15
σ away from µ = (15) / 15
σ away from µ = +1.00
In other words, our IQ score of 115 sits +1.00 standard deviations (σ) to the right of our mean (µ) of 100!
50% + 34% = 84%
Answer: With an IQ score of 115, you are smarter than 84% of the US population! This is because our value sits +1.00 σ away from the mean of all IQ scores.