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**STATS MIDTERM NOTES** Mean = Xbar = n (X i / n) i =1 _ Z-score = Z i = X i – X S Variance = S^2 = n _ (X i - X)^2 i =1 n-1 Standard deviation = sqrt(S^2) = S Empirical Rule: In a normal distribution, approx. 2/3 of the sample data are within one standard deviation of the mean in the interval (Xbar –S, Xbar +S). Approximately 95% of the data are X-bar +/- 2S, and almost all of the data are X-bar +/- 3S. To correctly describe a single quantitative variable : Center (Where is most of the data located? (If we had to pick one number, what would be the best representative?)), Spread (Over what range do we see most of the data? How good is our representation?), Skew (positive (right), negative (left), symmetric) (What direction does the spread extend to?), Weird things (outliers, multiple modes)(Are some points really far away? Do we have two centers?) Dot plot: easy to see all data points and to interpret, but gets messy and loses the big picture Measures of Central Tendency: the tendency of the data to cluster about certain numerical values; mean, median
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