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chapter1_print - Statistical Methods Chapter 1 Overview and...

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Statistical Methods Chapter 1: Overview and Descriptive Statistics General Introduction Statistics studies data, population, and samples. Descriptive Statistics vs Inferential Statistics. Descriptive Statistics Pictorial and tabular methods * Stemplot, dotplot, histogram, boxplot. Numerical measures * Measures of Location: Mean and Median. * Measures of Variability: Range, Variance, and IQR. Inferential Statistics Draw conclusions about a certain population parameter. * Confidence Intervals. * Hypothesis Testing. What does statistics study? Statistics is a mathematical science pertaining collection, presentation, analysis and interpretation of data . Population : a well-defined collection of objects. Sample : a subset of the population. Variable : characteristics of the objects. Observation : an observed value of a variable. Data : a collection of observations. statistics study data understand the population About Variable What is variable? Characteristics of a population of interest whose values vary. A variable can be Categorical e.g. x = gender of a person (male, female) Numerical Discrete variable: e.g. x = # of students in a class Continuous variable: e.g. x = height of a student
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Types of Data Data come from making observations either on a single variable or simultaneously on two or more variables. Univariate data: observations on a single variable Bivariate data: observations on two variables e.g. ( x, y ) = (height, weight) of a student Multivariate data: observations on more than two variables e.g. ( x, y, z ) = (height, weight, gen- der) of a student How to study data? What is Statistics? Data collection Sampling methods, experimental design. Data analysis, presentation & interpretation – Descriptive statistics - summarize and describe features of data * Visual methods: dotplot, pie chart, histogram. * Numerical methods: measures of location ( mean, median) and variation (range, vari- ance) – Inferential statistics - make inference about the population from samples * Point estimate, confidence intervals, hypothesis testing. Inferential Statistics and Probability Theory 2
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Descriptive Statistics: Visual Methods Stem-and-leaf display Dotplot Histogram Boxplot Stem-and-leaf Display Example 1 The number of touchdown passes thrown by each of the 31 teams in the National Football League in 2000 is given below: { 14, 29, 22, 18, 20, 15, 6, 9, 32, 18, 19, 18, 23, 28, 37, 21, 14, 19, 21, 20, 16, 22, 33, 28, 12, 18, 22, 14, 33, 21, 12 } What does the data tell? The tens digits called stems are arranged as a column to the left. The ones digits are listed to the right of each stem and are called leaves . 0|69 0|69 1|4858984962842 1|2244456888899 2|920381102821 2|001112223889 3|2733 3|2337 What can we say about the data set now? Most teams had 10 - 29 touchdown passes. Refined Stem-and-leaf Display When too many leaves are lumped into a few stems, splitting the stem helps reveal more information about the distribution of data. We can further ”refine” the above stem-and-leaf display by splitting each stem into two parts: low and high.
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