AP Stats Test Review #2 Focus: Measures of Center and Spread Outliers Boxplots Experiments Random Variables

Measures of Center and Spread Measures of Center are Mean and Median  Median is resistant to outliers (chop the outliers off)  Mean is non-resistant to outliers (better measure for approximately normal distributions) Measures of Spread are IQR and Standard Deviation  IQR goes with Median and Standard Deviation goes with Mean

Outliers Outliers are all data that are more than 1.5 IQR from Q 1 and Q 3.

Boxplots Boxplots are displays that show the 5 number summary Minimum Q 1 Median Q 3 Maximum Modified boxplots exclude the outliers.

)Find the measures of center and spread, 2)If 5 was added to each piece of data, what would the new measures of center and spread be? 3)If each piece of data was multiplied by 10, what would the new measures of center and spread be? 4)Calculate if there are any outliers in the data set. 5)Draw a modified boxplot for the data.

Answers: The median and IQR is more appropriate because data is skewed. 4)IQR = 20 – 16 = 4  1.5(IQR) = 6 Q 1 – 6 = 16 – 6 = 10  since 3 is less than 10, it is an outlier. Q = = 26  no data is over 26, so no outliers on this side.

Experiments An experiment is when a treatment is imposed. A study is when you observe a behavior (no treatment). In an experiment, you want to use a control or placebo when appropriate. Why? The Principles of Experiments are: 1) Control 2) Randomize 3) Replicate 4) Block when possible to reduce lurking variables

What is the definition of each term? Blinding (Single or Double) Level Factors Response variable

Blinding (Single or Double) – Not allowing the subjects and/or evaluators to know who is assigned to what treatment. Level – A variable whose values are controlled by the experimenter. (i.e. 400 mg, 800 mg, 1200 mg of aspirin) Factors – all the different treatments Response variable – the variable that is affected by the treatments (i.e. losing weight because of treatments)

You are interested in determining if daily doses of ibuprofen reduces the pain of arthritis in elderly people. You have 60 elderly people with arthritis who are willing to volunteer. In addition, you are going to administer 2 different doses of ibuprofen, 400 mg and 800 mg. You are also unsure if gender is a factor in the effectiveness of ibuprofen on arthritis. Design an experiment that takes all of these variables into account.

Random Variables X$3$5$8$0 P(x) A game is played by spinning a spinner with the values $3, $5, $8 and $0 with the following probabilities. What is the expected value and standard deviation of the winning?

Answers: Expected value = $4.45 Standard Deviation = $3.25

What happens when you add and subtract random variables?

Last Example The mean number of bolts needed to make a truck is 321 with a standard devation of 15 and the mean number of switches to build a truck is 23 with a standard deviation of 6. Find: a)the mean and standard deviation of bolts and switches to build one truck. b)the mean and standard deviation of bolts needed to make 3 trucks.

Answers: