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

2. 16.1 The Center of the Data Set
Center of the Data= sample mean:
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
Sample median is more robust in the presence of outliers.

4. Variability in A Data Set
Variance: Standard Deviation: where n is the number samples Why we choose the factor 1/(n−1) instead of 1/n will be explained later (in Chapter 19).

5. Variability cont. Medn= median of sample
Median of Absolute Deviation (MAD):
The Median of the Absolute Deviations of a Sample.
Medn= median of sample
Absolute Deviation:
The absolute value of the distance
Of a point xi in a data set from
the median

6. Empirical quantiles
The order statistics consist of the same elements as the original dataset x1, x2 x3,…, xk , but in ascending order. Denote by the kth element in the ordered list. Then: The pth quartile corresponds to pth quartile of a cdf: Finv(p) where F(p) is the cumulative distribution function of the data

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

9. 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

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