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+ Thursday February 10th, 2011 Thursday February 10th, 2011 Mind Buster: Sec. 1.3 (2.4) Bias in Surveys S C H E D U L E Sec. 1.3 Bias in Surveys M I N D Lesson: Sec. 1.4 (2.5) Measures of Central Tendency Time to practice new skills HandIn Your Sec. 1.3 Survey in Bias Section Summary B U S T E R 1) Identify the type of bias which would most likely occur in the following scenarios and justify: a) A student asks a principal if he/she has ever skipped school. b) A group of teenagers is given a survey on gardening techniques. c) Belle River is surveyed on their opinion of the new border crossing planned for the West end of Windsor. d) Mr. Pearce surveys how many students have completed their homework after warning the previous day that he would be checking homework. 2) Identify whether the following questions are loaded, causing potential bias or not: a) Do you believe the new mayor will be positive for the city? b) Do you eat a healthy sub for lunch or a greasy slice of pizza? c) Do you like Mr. Pearce as a teacher, even though he picks favourites? d) Should the school have a fundraiser for the Football team? Unit 1 Statistics of One Variable Consolidation: Sec. 1.4 (2.5) Measures of Central Tendency Pull L E S n S O N n Mean, median, and mode are considered to be measures of central tendency due to their ability to provide a central value which can summarize a set of data. MEDIAN MEAN Most commonly known n as the average The middle number in n an ordered list. μ=Ʃx Sample: x=Ʃx N n Tips: • There can be multiple modes if there are more than one value which occurs most often. • odd number of values: select middle value. • even number of values: take mean of middle two values. 90 84 95 64 71 70 83 45 73 51 68 Class B 54 80 12 61 73 69 92 81 80 61 75 74 15 44 91 63 50 84 a) Find the mean of both classes. b) Find the median of both classes. Class A 45 51 55 64 66 68 70 71 12 15 44 50 54 61 61 63 • Some data sets have no mode. Pull Ʃ = "Sigma" x= "xb Summation Sign ar" Ʃ x = Sum of all xvalues 71 71 73 76 82 83 84 90 95 74 75 80 80 81 84 91 Class B Pull Population: The most frequently occurring value in a data set. Class A 71 82 55 76 66 71 Pull Method: • Arrange data set in ascending order. Formula: μ= MODE Two classes, A and B, recently wrote the same data management exam and had the following marks: L E S S O N 69 73 92 au" "me c) Find the mode of both classes. Weighted Mean n Outliers n Some distributions of data outliers, which are values distant from the majority of the data. Pull Effect of Outliers on Measures of Central Tendency Median Mode Pull Pull Tend to drag the mean up Have little effect on the Have no effect in most median since a very large cases since most outliers or down, sometimes significantly due to a very or very small number will be do not repeat in a data set at the beginning or end of large or small number being added to the average the list in ascending order Example: Pull Mean The weighted mean is calculated in a similar manner to the mean, except values in certain groups or categories have more importance than others. Example: Sample of 7 students & their number of lates to class... Last semester, you had an 84% going into your final exam for English. You received a 75% on the final. Calculate your overall average (weighted mean) OUTLIER Pull Pull 1 22 22 4 5 6 8 20 Mark Category Pull Pull Mean x=4 6 Pull Pull 1 + 2 + 2 + 4 + 5 + 6 + 8 + 20 7 8 Median = 4 4.5 Mark % Weighting Factor, % Term Work 84 70 Exam 75 30 Mode = 2 Practice: Page 133135 #110, 12, 14 1