Math 145Math 145

September 11, 2006September 11, 2006

RecapRecap IndividualsIndividuals – are the objects described by – are the objects described by

a set of data. Individuals may be people, a set of data. Individuals may be people, but they may also be animals or things.but they may also be animals or things.

VariableVariable – a characteristic of an – a characteristic of an individual. A variable can take different individual. A variable can take different values for different individuals.values for different individuals.

Categorical variableCategorical variable – places an individual – places an individual into one of several groups or categories. into one of several groups or categories. {Gender, Blood Type}{Gender, Blood Type}

Quantitative variableQuantitative variable – takes numerical values – takes numerical values for which arithmetic operations such as for which arithmetic operations such as adding and averaging make sense. {Height, adding and averaging make sense. {Height, Income, Time, etc.}Income, Time, etc.}

Quantitative VariablesQuantitative Variables Discrete VariablesDiscrete Variables – There is a – There is a

gap between possible values.gap between possible values. Counts (no. of days, no. of people, Counts (no. of days, no. of people,

etc.)etc.) Age in yearsAge in years

Continuous VariablesContinuous Variables – – Variables that can take on Variables that can take on values in an interval.values in an interval.

Survival time, amount of rain in a Survival time, amount of rain in a month, distance, etc.month, distance, etc.

DistributionDistribution

- The distribution of a - The distribution of a variable tells us what values it variable tells us what values it takes and how often it takes these takes and how often it takes these valuesvalues

Categorical DataCategorical Data Table or Bar ChartTable or Bar Chart

Quantitative DataQuantitative Data Frequency TableFrequency Table HistogramHistogram Stem-and-leaf plotStem-and-leaf plot

Length of StayLength of Stay

5 1 15 9

3 7 2 12

4 18 9 13

28 24 13

1 6 10

5 6 9

Describing a Describing a distributiondistribution

SkewnessSkewness SymmetricSymmetric Skewed to the rightSkewed to the right Skewed to the leftSkewed to the left

Center/SpreadCenter/Spread No of peaks (modes)No of peaks (modes)

Unimodal, Bimodal, MultimodalUnimodal, Bimodal, Multimodal OutliersOutliers

Consider # 1.15, 1.17, 1.18 on page Consider # 1.15, 1.17, 1.18 on page 29.29.

Graphical ProceduresGraphical Procedures Categorical DataCategorical Data

Bar ChartBar Chart Pie ChartPie Chart

Quantitative DataQuantitative Data HistogramHistogram Stem-and-leaf plot (stemplot)Stem-and-leaf plot (stemplot) Time Plot (Time Series Data)Time Plot (Time Series Data)

A A time plottime plot of a variable plots of a variable plots each observation against the time at each observation against the time at which it was measured.which it was measured.

Consider example 1.11 on page 22.Consider example 1.11 on page 22.

HomeworkHomework

Exercises:

Sec 1: 1.1, 1.2, 1.3, 1.9, 1.11, 1.17, 1.19, 1.20

Section 1.2Section 1.2 Measures of CenterMeasures of Center

Mean (Average)Mean (Average)

{2.5, 3.2, 3.2, 3.4, 3.6, 3.7, 3.9, 3.9, {2.5, 3.2, 3.2, 3.4, 3.6, 3.7, 3.9, 3.9, 4, 4.2, 4.2}4, 4.2, 4.2}

MedianMedian Measures of SpreadMeasures of Spread

RangeRange Standard DeviationStandard Deviation Five-number summaryFive-number summary

Consider example 1.11 on page 22.Consider example 1.11 on page 22.

HomeworkHomework

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

Thank you!Thank you!