FANR 3000 1st Edition Lecture 5Outline of Last Lecture I. Measures of Central TendencyII. Measures of DispersionIII. Key Points Outline of Current Lecture I. Measures of Shape and Normal DistributionII. ShapeIII. Empirical Rule IV. Central Limit Theorem Current LectureI. 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 distributionof the data, using either one of the following:o Frequency distributiono Relative frequency distribution II. Shape- Symmetrical= normal distribution- Mean, median, mode are the same - Asymmetrical distributions: the direction of skewness depends on the location of the extreme valueso Mean exceeds the median and mode= positive or right-skewedo Mean is exceeded by the median and mode= negative or left-skewed- Box and Whisker plotso Represents the interquartile range from 50% of the datao 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.- Normal distribution: if the population is normally distributed, then a sample fromthe 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 III. Empirical Rulea. 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 mean2. The distributions of the sample means reflects a normal distribution3. The mean of sample means of the true mean of the populationIV. Central Limit Theorem a. As a sample size gets large enough, the sampling distribution of the mean can be approximated by the normal