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1.3 Standard Deviation & VarianceSample MeanM=∑ XnSum of SquaresSS=∑(X−µ)2Sample VarianceX−´X¿2¿Σ¿s2=SSn−1=¿Sample Standard Deviations=√s2
Examples:1.)A statistics teacher wants to decide whether or not to curve an exam. From her class of 300 students, she chose a sample of 10 students and their grades were:72, 88, 85, 81, 60, 54, 70, 72, 63, 43Find the mean, variance, and standard deviation for this sample.2.)Suppose the statistics teacher decides to curve the grades by adding 10 points to each score. What is the new mean, variance, and standard deviation?
´3.)Find the variance and the standard deviation of the following set of data (whose mean is 4.5).3, 6, 2, 7, 4, 5Mean= 4.5Standard Deviation= 1.871Variance= 3.5New Mean= 9New Standard Deviation= 3.742New Variance= 14
Sometimes we want to compare the variations between two groups. The Coefficient of Variationcan be used for this.The coefficient of variation is the ratioof the standard deviation to the mean. A smaller ratio willindicate less variation in the data. Example:4.)The following statistics were collected on two different groups of stock prices:Which can be said about the variability of each portfolio?$49.80=.059237→ less variationPortfolio APortfolio BSample size1015Sample mean$52.65$49.80Sample standard deviation$6.50$2.95Coefficient of Variation = (Standard Deviation) / (Mean)CoV A = $6.50$52.65=.123457CoV B = $2.95