An experiment consists of tossing a die and then ipping a coin once if the number on the die is even. If the number on the die is odd, the coin is ipped twice. Using the notation 4H, for example, to denote the outcome that the die comes up 4 and then the coin comes up heads, and 3HT to denote the outcome that the diecomes up 3 followed by a head and then a tail on the coin, construct a tree diagram to show the 18 elements of the sample space S.

Week 2 Being mathematically precise about describing quantitative value distribution Measuring center: MEAN - Mean: the arithmetic average The sample mean, which is a statistic, is denoted by X´ (“ex- bar”): X +X +…+X ∑ X X= 1 2 = i n n where n is the sample size - The population mean, which is a parameter, is denoted by μ (“mu”): x1+x 2…+x N ∑ xi μ= N = N where N is the population size - The mean is sensitive/nonresistant to outliers, it is pulled towards the tail in a skewed distribution MEDIAN - The mean cannot be very useful when you have big outlier(s), so we use the median to measure center - To find the median 1. Reorder data value from smallest to largest 2. If there are an odd # of values, the median is the middle value 3. If there are an even # of values, the median is the average of the two middle values - The median is relatively resistant to outliers and skewness, median will not be pulled towards that tail as greatly as the mean in a skewed distribution IN GENERAL - In a symmetric distribution mean and median are almost the same - For bell distributions (symmetric), the mean is appropriate. - For distributions with severe outliers and skewness, use median as measure of center - Use the mean as a measure of center whenever possible b/c is uses data values exactly, so it’s more mathematically useful Measuring spread: STANDARD DEVIATION - Standard deviation: typical/standard deviatio