1. Chapter 16 Exploratory data analysis: numerical summaries CIS 2033 Based on Textbook: A Modern Introduction to Probability and Statistics. 2007 Instructor: Dr. Longin Jan Latecki Slides: QUINCY R WALKER

2. 16.1 The Center of the Data Set Center of the Data= sample mean, sample median Mean: x bar n = the sample size Example: Sample mean of the following data is 44.7 43, 43, 41, 41, 41, 42, 43, 58, 58, 41, 41

3. Outliers an outlier is an observation that is numerically distant from the rest of the data

4. Variability in A Data Set Variance: Standard Deviation=sqrt(Var(X)): Where: n=number samples x bar =mean

5. Variability cont. Median of Absolute Deviation (MAD): The Median of the Absolute Deviations of a Sample. Med n = median of sample Absolute Deviation: The absolute value of the distance Of a point x[i] in a data set from the median

6. Empirical quantiles The order statistics consist of the same elements as the original dataset x 1, x 2 x 3,…, x k, but in ascending order. Denote by the kth element in the ordered list. Then: To compute the pth quartile use this formula: F inv (p) where F(p) is the cumulative distribution function

7. Quartiles Lower quartile: qn(.25) Upper quartile: qn(.75) Interquartile Range (IQR) IQR = qn(0.75) − qn(0.25) Median(Middle Quartile): qn(.50)

8. The box-and-whisker plot Advantages: Good representation of statistical data Shows quartiles, median and outliers Disadvantages poor graphical display of the dataset histogram and kernel density estimate are more informative displays of a single dataset

9. Using boxplots to compare several datasets Boxplots become useful if we want to compare several sets of data in a simple graphical display: