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I can identify and draw conclusions with mean, median, percentile, quartiles, range, standard deviation, variance, inter-quartile range and outliers. 1 Ch. 1 Day 3 Sec 1.2 Mean = Average "xbar" or Median M = Midpoint 1. Order Sm to Lrg 2. If odd # of observations, middle # 3. If even # of observations, mean of 2 middle numbers * Median is not affected (as much)by outliers. The mean is affected by outliers. Find the Mean and Median Ex. 2, 4, 8, 10 now compare to data 2, 4, 8, 10, 26 2 Find the Mean and Median with the TI 84 IQ Test scores 11 randomly selected 7th graders. 114, 100, 104, 89, 102, 91, 114, 114, 103, 105, 108 Mean Sum of the observations Sum of the observations squared Standard Deviation Population Deviation Number of Observations 3 If data is exactly symmetric the mean = median M If data is skewed left, mean < median M If data is skewed right, mean > median M 4 5 Number Summary Min, Q1, Med, Q3, Max When to use? When you have skewed data, using the Median to describe the center. IQR Inter Quartile Range Q3 Q1 Spread of the middle 50% Outlier If a point is more than 1.5(Q3 Q1) from Q1 or Q3, then it is an outlier Find the 5 # summary for the number of HR's hit by Barry Bonds 16 19 24 25 25 33 33 34 34 37 37 40 42 46 49 73 Draw a Boxplot with the 5 # summary 5 Find the 5 # summary for the number of HR's hit by Barry Bonds with the TI 16 19 24 25 25 33 33 34 34 37 37 40 42 46 49 73 Draw a Boxplot with the TI 6 Standard Deviation Used to describe the spread of data when using the mean to describe the center. Standard Deviation is the average spread of data from the mean. n-1 represents the degrees of freedom When s=0, there is no spread s>0 Always! Why? As observations become more spread out, s will increase. Variance - is the Standard Deviation squared 7 I can identify and draw conclusions with mean, median, percentile, quartiles, range, standard deviation, variance, inter-quartile range and outliers. 8