L5

• The z-score is a measure of how many standard deviations a data point is from the mean, calculated by subtracting the mean from the data point and then dividing the result by the standard deviation

  
• The standard normal distribution is a bell-shaped curve with a mean of 0 and a standard deviation of 1, used to model various types of data like heights, weights, and test scores

  
• The table of the standard normal distribution shows the proportion of the distribution that lies beyond a given z-score, aiding in understanding the percentage of data points above or below a certain standard deviation from the mean

  
• A right skew in a distribution means the data is spread out more to the right than to the left, with the mean being pulled towards the tail of the distribution, making it greater than the median

  
• Kurtosis indicates how data are bunched together or spread out, with leptokurtic data being bunched together and platykurtic data being spread out

  
• Tests of normality include the Shapiro-Wilk, Kolmogorov-Smirnov, Anderson-Darling, and Lillefor’s tests, used to determine if a distribution is normal or not
• When data are not normally distributed, transformations like log or square root can be applied to improve normality, especially if the data show skewness or heteroscedasticity
• log transformation

  -linearize relationships