HW Chapter 3: Describing, Exploring & Comparing Data Descriptive Statistics Summarize or describe the important characteristics of a known set of data (center, variation, distribution, and outliers) Inferential Statistics Use sample data to make inferences (or generalizations) about a population. 3 – 2 Measures of center or central tendency Definition : Measure of Center - A value at the center or middle of a data set. Rounding Rule: Round to ____ more place than is present in the original data Mean, Median, Mode, and Midrange from Raw Data (Ungrouped Data) Mean = the measure of center obtained by adding the values and dividing the total by the number of values. Notation Population mean (mu): µ = --------- Sample mean (x-bar): x = ------- N = population size, n = sample size, n = + + + ∑ x = Sum of all data values = ∑ xi x1 x2 ... xn = individual data values i=1 Median ( ~x = x – tilde) = the value that lies in the middle of the data when arranged in ascending order. To find the median, first sort the data values (arrange them in order of increasing. Then, follow one of these two procedures: 1) n is odd: Median = Value of the middle term 2) n is even: Median = Mean of the two middle terms Important to note: 1 Mode = the value with ____________________________ . a) ___________: Having 2 modes (same highest frequency). b) ___________: Having more than 2 modes. c) ___________: When each value appears only once (does not repeat). Important Note: ___________________________________________________________ Midrange (MR) The measure of center that is the value ________between the highest and lowest values in the original data set. (Sensitive to outliers like the Mean) Hi + Low Midrange = 2 Important to note: Example 1 : 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, 43 a) Compute the population mean of this data. Be sure to label with correct notation (mu or x-bar) and round to the proper place value. b) Compute the median of this data. Continue to label and round appropriately. Example 2: Suppose the start-up company hires a new employee. The travel time of the new employee is 70 minutes. Determine the mean and median of the “new” data set. LABEL solutions. 23, 36, 23, 18, 5, 26, 43, 70 Example 3: a) Find the mode: 27, 55, 88, 27, 99, 27, 55, 55, 88 b) Find the mode: 1, 2, 3, 5, 6, 7, 8, 9 Example 4: The followings are measured amounts of lead in the air. Find the midrange for this sample: 5.4, 1.10, 0.42, 0.73, 0.48, 1.10 2.