1. Warm Up Pick the correct statement Group A 2, 1, 4, 8, 5, 4
Group B 4, 3, 1, 4, 6, 9
1. Group A has a larger mean and std. dev.
2. Group A has a larger mean but smaller std. dev
3. Group B has a larger mean and std. dev
4. Group B has a larger mean but smaller std.

2. How can we apply the empirical rule to real life examples?
Math II Day 2 (1-5-11)
Standard MM2D1C
Use means and standard deviations to compare data sets
Today’s Question:
How can we apply the empirical rule to real life examples?

3. Box and Whisker to Bell Curve
Total area under the curve is 100%

4. The curve is the same as a bar graph

6. Let’s involve Standard Deviation

7. Compare the Class Heights
Height of 2nd Period students
Height of 4th Period students
5’-0” ’-6” ’-10” ’-2” ’-6”

8. Empirical Rule/Normal Distribution
Nearly all values lie within 3 standard deviations of the mean.
About 68% of the values lie within 1 standard deviation of the mean. In statistical notation, this is represented as:
About 95% of the values lie within 2 standard deviations of the mean. The statistical notation for this is:
Nearly all (99.7%) of the values lie within 3 standard deviations of the mean. Statisticians use the following notation to represent this:

9. Empirical Rule

10. In other words

11. Normal Distributions found in Nature
Heights of Women
Weights of Men
Shoe size of all 15 year olds
IQ’s
Time it takes for me to run a mile.
Licks to get to the center of a tootsie pop.

12. The greater our sample size, the more these things will start to look normal
Let's see it in action

13. Shoe sizes example Mean = 10 Standard Deviation = 2
What percentage of men have a shoe size:
Greater than 10
Less than 12
Between 6 and 14

14. Classwork
Pg 266 #1 – 11