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CANDY STATISTICS – Pre-Test Key (Algebra I) Reorder the Data Set: {3, 5, 6, 7, 8, 9, 10, 11, 12, 12, 12, 24} Note: Teacher can change data set, if needed. 1.) What is the mean of the data set? (3+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 12+ 12+ 24)/12 = (119)/12 = 9.9 2.) What is the median of the data set? {3, 5, 6, 7, 8, 9 | 10, 11, 12, 12, 12, 24} => Median = 9.5 3.) What is the mode of the data set? {3, 5, 6, 7, 8, 9, 10, 11, 12, 12, 12, 24} => Mode = 12 4.) Divide the data set into Quartiles with data points arranged from smallest to largest. What is the Interquartile Range (IQR) of the data set? 3, 5, 6 | 7, 8, 9 | 10, 11, 12 | 12, 12, 24 Q1 is the average of 6 & 7 = 6.5 Q2 is the average of 9 & 10 = 9.5 Q3 is the average of 12 & 12 = 12 IQR = Q3-Q1 = 12-6.5 = 5.5 5.) Is the data point 24 an outlier? Explain. Use Outlier Formula to check: Is 24 > Q3 + 1.5(IQR)? If so, it is an outlier. Q3 + 1.5(IQR) = 12 + 1.5(5.5) = 12+8.25 = 20.25 Since 24 > 20.25, YES, it is an outlier. 6.) The standard deviation of the data set has been calculated and found to be 5.3. Explain what this tells us about the data set. Assuming this data has a normal distribution: A Standard Deviation of 5.3 indicates that ~68.26% of the data points are ±5.3 units away from the Mean (= 9.9). The shape of the normal distribution curve would be: 1 Notes: If a data set has a lot of values on the extreme far right compared to the other data points, then it will be “Left-Skewed” because the tail is on the left. Example: {3, 5, 6, 7, 8, 9, 10, 11, 12, 12, 12, 24, 68, 85, 102} If a data set has a lot of values on the extreme far left compared to the other data points, then it “Right-Skewed” because the tail is on the right. Example: {0.1, 0.2, 0.5, 3, 5, 6, 7, 8, 9, 10, 11, 12, 12, 12, 24} A version of this figure is located on the University of South Alabama website: http://www.southalabama.edu/coe/bset/johnson/lectures/lec15.htm. 2