Empirical Rule (3 Sigma Rule)
• A statistical rule stating that for a
normal distribution almost all data will
fall within 3 standard deviations of the
mean.
• Normal Distribution- the spread of
the data is symmetric
BELLWORK
1. Use the data to find a) MEAN b) MODE
d) IQR e) 5 NUMBER SUMMARY
f) VARIANCE AND STANDARD DEVIATION.
16 10 2 7 4 14 12
2.Plot a box and whisker .Is the data symmetric
skewed left or right?
3. What do you notice about the mean mode
and median?
Empirical Rule
* 68% of the data values fall within 1 standard deviation of the
mean in either direction
* 95% of the data values fall within 2 standard deviation of the
mean in either direction
* 99.7% of the
data values fall
within 3 standard
deviation of the
mean in either
direction
68%
95%
99.7%
𝑥 − 3𝑠
𝑥 − 2𝑠
𝑥−𝑠
𝑥+𝑠
𝑥 + 2𝑠
68-95-99.7% RULE
𝑥 + 3𝑠
Empirical Rule applies only to SYMMETRIC distributions
Average American adult male height is 69 inches (5’ 9”)
tall with a standard deviation of 2.5 inches.
----|------------|-----------|-----------|-----------|-----------|-----------|---𝑥
1) What percent of the adult males have a height between 64
and 74 inches?
2) Between what two heights will 68% of all adult males fall?
Does the Empirical Rule apply to ANY type of
distribution?
* Empirical Rule Task