Section 1



Section 3.2 – Measures of DispersionFrom the example about McDonald’s and Wendy’s wait times, which one appears more dispersed? Which line would you prefer to wait in? Why?Identify Objective 1:What is the range?State the formula for finding the range:Example: Finding the Range of a Set of Data.The following data represent the travel times (in minutes) to work for all seven employees of a start-up web development company. Find the range. 23, 36, 23, 18, 5, 26, 43Identify Objective 2:What is the population standard deviation?What variable is used to represent the population standard deviation?______Formula:Computational Formula:Example: Computing a Population Standard Deviation.The following data represent the travel times (in minutes) to work for all seven employees of a start-up web development company.23, 36, 23, 18, 5, 26, 43Compute the population standard deviation of this data.xi?(xi – ?)(xi – ?)22336231852643What is the sample standard deviation?What variable is used to represent the sample standard deviation?______Formula:Computational Formula:What is the degrees of freedom?Example: Computing a Sample Standard Deviation.Here are the results of a random sample taken from the travel times (in minutes) to work for all seven employees of a start-up web development company:5, 26, 36Find the sample standard deviation.Example: Comparing Standard Deviations.Determine the standard deviation waiting time for Wendy’s and McDonald’s. Which is larger? Why?Wait Time at Wendy’s1.500.791.011.660.940.672.531.201.460.890.950.901.882.941.401.331.200.843.991.901.001.540.990.350.901.230.921.091.722.00Wait Time at McDonald’s3.500.000.380.431.823.040.000.260.140.602.332.541.970.712.224.540.800.500.000.280.441.380.921.173.082.750.363.102.190.23Technology Step-By-Step: Determining the Standard DeviationIdentify Objective 3:What is the variance?What symbol is used to represent the population variance?___, the sample variance?____Example: Computing a Population Variance.The following data represent the travel times (in minutes) to work for all seven employees of a start-up web development company.23, 36, 23, 18, 5, 26, 43Compute the population and sample variance of this data. Identify Objective 4:What is the empirical rule? (Draw and label a curve.) Example: Using the Empirical Rule.From data representing the serum HDL cholesterol of the 54 female patients of a family doctor we found a mean of 57.4 and a standard deviation of 11.7. (a) Determine the percentage of all patients that have serum HDL between 45.7 and 69.1 according to the Empirical Rule. (b) Determine the percentage of all patients that have serum HDL of less than 34 and greater than 80.8 according to the Empirical Rule.(c) Determine the percentage of all patients that have serum HDL greater than 80.8 according to the Empirical Rule. Identify Objective 5:State Chebyshev’s Inequality:What does the letter k stand for?What type of data can we use Chebyshev’s inequality for?Example: Using Chebyshev’s Theorem.Recall from the previous example that from the serum HDL cholesterol of the 54 female patients of a family doctor we found a mean of 57.4 and a standard deviation of 11.7. Use Chebyshev’s Theorem to(a) determine the percentage of patients that have serum HDL within 3 standard deviations of the mean. (b) determine the minimum percentage of patients that have serum HDL between 34 and 80.8. ................
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