Elementary Statistics Course Notes

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  • Topic: Sampling, Sample, Stratified sampling
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Chapter 1 The nature of Probability and Statistics

Basics of Statistics: 1. Statistics: It is the science of conducting studies to collect, organize, summarize, analyze and draw conclusions from data. In another words, it is a scientific field of study that provides approaches to making inferences about populations based on the examinations of smaller sets of data. a. Descriptive statistics: It consists of the collection, organization, summarization and presentation of data. Examples: sample mean, median, range, standard deviation, charts, graphs, tables, etc. b. Inferential statistics: It consists of generalizing from samples to population, performing estimations and hypothesis tests, determining relationships among variables, and making predictions. Examples: Analysis of variance, test of goodness of fit, etc. 2. Goals of Statistics:  To study the population  To study the variation  To present the data in reduced form  To apply Statistics as a research tool 3. Variable: It is the representation of some characteristic of an individual that can be measured or recorded and generally can take multiple values. Examples: height, weight, etc of people. Variables whose values are determined by chance are called random variables. a. Qualitative variables (categorical variables): They are the variables which can be places into distinct categories according to some characteristics or attribute. Examples: Gender (male or female), religious affiliation (protestant, catholic, Jewish, Muslim, Buddhists, Hindus, Other, None), favorite type of music (Classical, Country, folk, Jazz, rock, etc), etc. b. Quantitative variables: They are numerical variables and can be ordered or rank. It can be further classified into two categories: i. Discrete variables: They assume values that can be counted. It has possible values from a set of separate numbers. Examples: number of children in a family, number of car accidents in Greeley, CO in December, 2010, etc.

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Continuous variables: They can assume an infinite number of values (infinite continuum of possible real number values) between any two specific values. They often include fractions and decimals. Examples: temperature, subject’s annual income, etc.

4. Data (singular datum): They are numbers with a context. Context is the setting (circumstances) that give rise to the numbers. Both numbers and context are necessary to have data. A collection of data values is called data set while each value in the data set is called a datum. 5. Population: It consists of all subjects that are being studied. So, it is a group of elements (people, objects, animals, equipment, etc) whose measurements are interest. A value calculated from an entire population is called parameter. Most of the time due to expense, time, size of population, etc, it is not possible to use entire population for a statistical study. So, researchers use samples.

6. Sample: It is a group of subjects selected from a population. So, it is a subset of population in which data is collected in order to learn more about the population. Hopefully, the sample is representative of the population. A value calculated from sample data is called statistic. Measurement scales: 1. Nominal level of measurement: It classifies data into mutually exclusive (nonoverlapping), exhausting (union makes sample space) categories in which no order or ranking can be imposed on the data. The scale does not have a high or low end. This scale contains the least amount of information. Examples: mode of transportation to work (automobile, bus, subway, bicycle, walk), classifying residents according to zip code, religious beliefs (Christianity, Islam, etc.), marital status (married, single, divorced), etc. Ordinal level of measurement: This scale classifies data into categories that can be ranked or ordered; however precise differences between the ranks do not exist. There is no defined distance between levels. The distances between...
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