Analyzing Summarizing Data Numerical Measures categorical variables analysis

• Analyzing & Summarizing Data: Numerical Measures – categorical variables: • analysis consists of computing frequencies and/or relative frequencies and then drawing bar graphs • if the variable is ordinal, then median makes sense – quantitative variables • center - see Fig. 3. 17 (p. 71) for relationships – mode - most frequently occurring value of the variable – mean (arithmetic average) – trimmed mean (trim off the lowest and highest x%) – median (50 th percentile) • variability - see Fig. 3. 18 (p. 74) – range = max. value of the variable minus the min. value – percentiles, in particular Q 1 and Q 3 (the quartiles); IQR – quantile plots: see R#1 for an explanation of how to do these plot in R

• Analyzing & Summarizing Data: Numerical Measures – the standard deviation is another measure of variability it measures the spread of the data around the mean notice that if the y’s are close together s will be close to zero, and if the y’s are spread out, s will be much greater than zero. – for “mound-shaped” distributions, the Empirical Rule describes the relationship between the mean and the standard deviation (see p. 81) and the histograms on page 82 in Figure 3. 24. • HW (thru 3. 6): #3. 1 b, 3. 4, 3. 6, 3. 10, 3. 17, 3. 18, 3. 22, 3. 26, 3. 27, 3. 28, 3. 38 -3. 40