Empirical Rule (3 Sigma Rule)

1. 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

2. BELLWORK 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?

3. Empirical Rule * 68% of the data values fall within 1standard deviation of the mean in either direction * 95% of the data values fall within 2standard deviation of the mean in either direction * 99.7% of the data values fall within 3standard deviation of the mean in either direction 68% 95% 99.7% 68-95-99.7% RULE

4. Empirical Rule applies only to SYMMETRIC distributions

5. Average American adult male height is 69 inches (5’ 9”) tall with a standard deviation of 2.5 inches. ----|------------|-----------|-----------|-----------|-----------|-----------|---- What percent of the adult males have a height between 64 and 74 inches? Between what two heights will 68% of all adult males fall?

6. Does the Empirical Rule apply to ANY type of distribution? * Empirical Rule Task