1. Math 341
January 24, 2007

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 5 1 15 9 3 7 2 12 4 18 13 28 24 6 10

6. Fifth-grade IQ Scores
145
101
123
106
117
102
139
142 94
124 90
108
126
134
100
115
103
110
122
136
133
114
128
125
112
109
116
130
131 96
127
113
105
118 81 97 82
137 89

7. Describing a distribution
Skewness
Symmetric
Skewed to the right (positively skewed)
Skewed to the left (negatively skewed)
Center/Spread
No of peaks (modes)
Unimodal, Bimodal, Multimodal.
Outliers
Extreme values.

8. Graphical Procedures Categorical Data Quantitative 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 1.7 on page 14.

9. Section 1.3 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}
- sensitive to outliers.
Median – middle value
Mode – most frequent occurring value.

10. Homework Exercises: Sec 1: 4, 7, 8, 9. (pp. 10-11)

11. Section 1.4 Consider 3 samples Measures of Dispersion (Spread)
{1,2,5,5,8,9}
{3,4,5,5,6,7}
{5,5,5,5,5,5}
Measures of Dispersion (Spread)
Range
Variance
Standard Deviation
Five-number summary

12. Thank you!