FANR 3000 1st Edition Lecture 5 Outline of Last Lecture I Measures of Central Tendency II Measures of Dispersion III Key Points Outline of Current Lecture I Measures of Shape and Normal Distribution II Shape III Empirical Rule IV Central Limit Theorem Current Lecture I II Measures of Shape and Normal Distribution Measures of location Measures of dispersion The best way to judge shape is to examine the polygon related to the distribution of the data using either one of the following o Frequency distribution o Relative frequency distribution Shape Symmetrical normal distribution Mean median mode are the same Asymmetrical distributions the direction of skewness depends on the location of the extreme values o Mean exceeds the median and mode positive or right skewed o Mean is exceeded by the median and mode negative or left skewed Box and Whisker plots o Represents the interquartile range from 50 of the data o Whiskers at either end represent the remaining two 25 ranges of data These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute III IV Normal distribution if the population is normally distributed then a sample from the population should also be normally distributed regardless of the sample size o Standard deviation changes the shape of a bell curve 68 of values are within one standard deviation of the mean 95 values are within 2 standard deviations away from the mean 99 7 of values are within 3 standard deviations of the mean Empirical Rule a If the data is normally distributed the standard deviation can tell us a lot b Sampling distribution the lists of all possible samples and their associated sample mean i Increase in sample size the closer at getting the true sample mean 1 The sample mean is an unbiased estimator of the population mean 2 The distributions of the sample means reflects a normal distribution 3 The mean of sample means of the true mean of the population Central Limit Theorem a As a sample size gets large enough the sampling distribution of the mean can be approximated by the normal distribution