Section 1 - SAILS / DUAL CREDIT



Section 3.1 – Measures of Central TendencyIdentify Objective 1:What is the arithmetic mean?Give the formulas for finding population mean:sample mean:Example: Computing a Population Mean and a Sample MeanThe 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 mean of this data.Obtain a simple random sample of size n = 3 from the population of seven employees. Use this simple random sample to determine a sample mean. Find a second simple random sample and determine the sample mean. Identify Objective 2:What is the median value of a data set?Steps in Computing the Median of a Data Set: Step 1: Step 2:Step 3: For an odd number of data values in the distribution,Median = For an even number of data values in the distribution,Median = Example: Computing a Median of a Data Set with an Odd Number of ObservationsThe 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, 43Determine the median of this data.Example: Computing a Median of a Data Set with an Even Number of ObservationsSuppose the start-up company hires a new employee. The travel time of the new employee is 70 minutes. Determine the median of the “new” data set. 23, 36, 23, 18, 5, 26, 43, 70Technology Step-by-Step: Determing the Mean and Median:Identify Objective 3:Example: Computing a Median of a Data Set with an Even Number of ObservationsThe 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, 43Suppose a new employee is hired who has a 130 minute commute. How does this impact the value of the mean and median? What does it mean for a measure to be resistant?Relationship between the Mean, Median, and Distribution ShapeDistribution ShapeMean versus MedianSkewed Left Symmetric Skewed RightExample: Describing the Shape of the DistributionThe following data represent the asking price of homes for sale in Lincoln, NE. Find the mean and median. Use the mean and median to identify the shape of the distribution. Verify your result by drawing a histogram of the data.Identify Objective 4:What is the mode of a data set?How many modes can a data set have?Example: Finding the mode of a Data SetThe following data represent the number of O-ring failures on the shuttle Columbia for its 17 flights prior to its fatal flight:0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 3Find the mode number of O-ring failures.Example: Finding the mode of a Data SetFind the mode of exam score data listed below:82, 77, 90, 71, 62, 68, 74, 84, 94, 88When should you use the following measure of central tendency:Mean?Median?Mode? ................
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