Mr. Markwalter

 People who keep organized notebooks are doing the best  People who copy down my examples are doing the best  People who ask questions are doing the best  ∴Take our a notebook. No more loose leaf  I will start putting up models for note-taking

 We can make histograms of data.  But sometimes we have a lot of data and: THE OVERALL PATTERN OF A LARGE NUMBER OF OBSERVATIONS IS SO REGULAR WE CAN DESCRIBE IT BY A SMOOT CURVE!

 947 students tested  Distribution of scores is below

 We can look at it in the raw numbers OR  We can fit a curve (in red) that is a good model

 If we shade all the scores less than 6, what percentage of scores do you think we shaded?

 30.3% or 287 people out of 947  That means the total area of the bars would be 100% or a proportion of 1! 30.3%

 If we want to talk about the red curve, we make the total area below the curve %

 The area below the curve less than 6 is  That is 29.3% of the area which is less than %

 The curve is a pretty good model for the bars! 30.3%29.3%

 Is always on or above the horizontal axis  Has an area of 1 underneath it  A density curve describes the overall pattern of distribution.  The area under the curve and above any interval is the proportion of observations that fall in that interval.

 Mean is the balancing point of the curve  Median is the marker of equal areas; divides the area under the curve in half.

 If the area to the left line in the density curve shown below is 0.40, what is the area of the other part? 0.40

 What percentage of observations are to the left of the line in the curve below? 0.40

 There is one kind of curve that trumps them all.  We see it more than anything else  It is the basis of 95% of statistics.

 Describe Normal Distributions  They are defined by two numbers  Mean: μ  Standard Deviation: σ (the average distance from the mean)  Bell Shaped

 They are defined by two numbers  Mean: μ  Standard Deviation: σ  Bell Shaped

 As usual, the area under the curve is 1  Let’s take a look.  stat.stanford.edu/~naras/jsm/NormalDensity /NormalDensity.html stat.stanford.edu/~naras/jsm/NormalDensity /NormalDensity.html

 In the Normal distribution with mean μ and standard deviation σ: About 68% of observations fall within σ of μ. About 95% of observations fall within 2σ of μ. About 99.7% of observations fall within 3σ of μ.

 Usually we define a Normal curve like this  N(μ, σ)  N(6, 1) means we have a curve with mean 6 and standard deviation 1.  Using our Rule… 6-1=5 and 6+1=7 68% of the observations are between 5 and 7.

 I make candies. The mean mass of the candy is 100g and the standard deviation is 5.  Draw a Normal curve for the situation.  What percentage of candies is between 95g and 105g?  What percentage of candies is less than 105g?

 I make throw frisbees. My mean throw is 75 yards with a standard deviation of 5 yards  Draw a Normal curve for the situation.  What percentage of throws is between 65 and 85 yards?  What percentage of throws is less than above 70 yards?

 Spend 15 minutes doing this worksheet.  You may work with those around you.  If you do not finish it is homework.

 1, 4, 5, 5, 6, 9  Find the standard deviation