Math 341 January 24, 2007

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.}

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.

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

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

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

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.

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.

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.

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

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

Thank you!