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Elementary Statistics (Math 145)

Elementary Statistics (Math 145). September 9, 2010. Statistics. is the science of collecting, analyzing, interpreting, and presenting data . Two kinds of Statistics: Descriptive Statistics. Inferential Statistics.

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Elementary Statistics (Math 145)

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  1. Elementary Statistics(Math 145) September 9, 2010

  2. Statistics is the science of collecting, analyzing, interpreting, and presenting data. Two kinds of Statistics: • Descriptive Statistics. • Inferential Statistics. A statistical inference is an estimate, prediction, or some other generalization about a population based on information contained in the sample.  Use arepresentative sample.

  3. Methods of Acquiring Information • Published Source • Census • Sampling • Observational Study – researchers observe characteristics and take measurements, as in sample survey. (Association) • Designed Experiment – researchers impose treatments and controls and then observe characteristics and take measurements. (Cause and Effect)  Consider: #1.27 (p.21), #1.29

  4. Sampling Designs • Simple Random Sampling. • Systematic Random Sampling. • Cluster Sampling. • Stratified Random Sampling with Proportional Allocation.

  5. Descriptive Statistics • 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 (Qualitative) 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.}  Consider: #1.18 (p. 20), #1.21 (p.21)

  6. 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.

  7. Graphical Procedures • Categorical (Qualitative) Data • Bar Chart • Pie Chart • Quantitative Data • Histogram • Stem-and-leaf plot (Stemplot) • Dotplot • These plots describe the distribution of a variable.

  8. Length of Stay

  9. Fifth-grade IQ Scores

  10. 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

  11. 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.

  12. Chapter 1 : (pp. 19-23)# 1, 2, 5, 7, 10, 11, 12, 13, 16, 24, 28. Chapter 2 : (pp. 34-38) # 5, 6, 10. (pp. 45-50) # 25, 28. Homework

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