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.

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?

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

The curve is the same as a bar graph

Let’s involve Standard Deviation

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

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:

Empirical Rule

In other words

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.

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

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

Classwork Pg 266 #1 – 11