SOCY201 Lecture Notes 2 21 2012 Z Scores and Normal Curves Density Curves Scores of many students on test have regular distribution Distribution is symmetrical both tails fall off smoothly from a center point no large gaps no Smooth curve drawn through tops of histogram bars is a good description of overall pattern obvious outlying observations of the data Probability Density Curves Probability distribution identifies wither the probability of each value of a random variable when variable discrete or the probability of the value falling within a particular interval when variable continuous o Probability distribution describes range of possible values that a random variable can attain and the probability that the value of the random variable is within any subset of that range Smooth curve is used to describe proportion of observations that fall within ranges of values not counts of observations o Areas under the curve represent proportions of the observations these proportions are probabilities o Smooth curve is a density curve for the distribution Total area under curve 1 Normal Distributions One type of density curve is normal curve describe normal distributions Normal distributions have same overall bell shape symmetrical single peaked unimodal constant area between any 2 points Standardizing To standardize a value subtract mean of distribution then divide by standard deviation termed z transformation o Mean of a distribution transformed to z is 0 o Standard deviation of distribution transformed to z is 1 o Transforming distribution to z doesn t make distribution normal nor change relative position of cases within distribution SOCY201 Lecture Notes 2 21 2012 Z Scores and Normal Curves Density Curves Scores of many students on test have regular distribution Distribution is symmetrical both tails fall off smoothly from a center point no large gaps no Smooth curve drawn through tops of histogram bars is a good description of overall pattern obvious outlying observations of the data Probability Density Curves Probability distribution identifies wither the probability of each value of a random variable when variable discrete or the probability of the value falling within a particular interval when variable continuous o Probability distribution describes range of possible values that a random variable can attain and the probability that the value of the random variable is within any subset of that range Smooth curve is used to describe proportion of observations that fall within ranges of values not counts of observations o Areas under the curve represent proportions of the observations these proportions are probabilities o Smooth curve is a density curve for the distribution Total area under curve 1 Normal Distributions One type of density curve is normal curve describe normal distributions Normal distributions have same overall bell shape symmetrical single peaked unimodal constant area between any 2 points Standardizing To standardize a value subtract mean of distribution then divide by standard deviation termed z transformation o Mean of a distribution transformed to z is 0 o Standard deviation of distribution transformed to z is 1 o Transforming distribution to z doesn t make distribution normal nor change relative position of cases within distribution