1. Math 145 September 11, 2006

2. Recap  Individuals – are the objects described by a set of data. Individuals may be people, but they may also be animals or things.  Variable – a characteristic of an individual. A variable can take different values for different individuals.  Categorical variable – places an individual into one of several groups or categories. {Gender, Blood Type}  Quantitative variable – takes numerical values for which arithmetic operations such as adding and averaging make sense. {Height, Income, Time, etc.}

3. Quantitative Variables  Discrete Variables – There is a gap between possible values.  Counts (no. of days, no. of people, etc.)  Age in years  Continuous Variables – Variables that can take on values in an interval.  Survival time, amount of rain in a month, distance, etc.

4. Distribution - The distribution of a variable tells us what values it takes and how often it takes these values  Categorical Data  Table or Bar Chart  Quantitative Data  Frequency Table  Histogram  Stem-and-leaf plot

5. Length of Stay 51159 37212 418913 282413 1610 569

6. Describing a distribution  Skewness  Symmetric  Skewed to the right  Skewed to the left  Center/Spread  No of peaks (modes)  Unimodal, Bimodal, Multimodal  Outliers Consider # 1.15, 1.17, 1.18 on page 29.

7. Graphical Procedures  Categorical Data  Bar Chart  Pie Chart  Quantitative Data  Histogram  Stem-and-leaf plot (stemplot)  Time Plot (Time Series Data) A time plot of a variable plots each observation against the time at which it was measured.  Consider example 1.11 on page 22.

8. Homework Exercises: Sec 1: 1.1, 1.2, 1.3, 1.9, 1.11, 1.17, 1.19, 1.20

9. Section 1.2  Measures of Center  Mean (Average) {2.5, 3.2, 3.2, 3.4, 3.6, 3.7, 3.9, 3.9, 4, 4.2, 4.2}  Median  Measures of Spread  Range  Standard Deviation  Five-number summary Consider example 1.11 on page 22.

10. Homework Exercises: Sec 1: 1.1, 1.2, 1.3, 1.9, 1.11, 1.17, 1.19, 1.20 Sec 2: 1.42, 1.45, 1.47, 1.55-1.57*, 1.60, 1.62 Sec3: 1.78, 1.80, 1.81, 1.82, 1.83, 1.85*, 1.87, 1.89, 1.90*, 1.93-95, 1.97, 1.110, 1.115

11. Thank you!