Statistical Methods STAT 302 Chapter 1 Introduction to Statistics Copyright 2025 by Aburweis All rights reserved No part of this work may be reproduced in any form without written permission Course Learning Objectives By the end of this course students will recognize that statistics plays a central role in fostering critical thinking both within academic contexts and in professional and everyday decision making My objective is to leave you with the impression that the time you spend studying this subject will reward you in various ways and help you become an informed user of numerical information 2 Chapter 1 Learning Objectives Understand and use the fundamental terminology and vocabulary of statistics Differentiate between descriptive and inferential statistics Distinguish among populations samples parameters and statistics Classify variables as qualitative or quantitative and further categorize them as nominal ordinal discrete or continuous Understand and apply the appropriate levels of measurement in statistical analysis Demonstrate knowledge of fundamental sampling techniques and their use in research Collect organize and analyze data through well designed statistical studies 3 What is Statistics Do you think statistics is just about calculating batting averages at a baseball game tabulating Gallup poll results or tracking unemployment figures Or simply a college requirement The answer is unequivocally NO Statistics is a powerful and practical science with wide ranging applications in business government and the social medical and physical sciences Definition of Statistics Statistics is the science of collecting classifying organizing summarizing analyzing and interpreting data to make informed decisions 4 Why Should We Study Statistics Statistics provides us with tools to navigate the overwhelming amount of data encountered in various aspects of life Source https www malwarebytes com blog news 2018 12 2018 the year of the data breach tsunami 5 The Importance of Statistics in the Modern World Questions Statistics Can Answer Learning Statistics can help On average do individuals who consume high fiber cereal for breakfast weigh less than those who skip breakfast Develop a clearer understanding of information encountered in daily life Sports politics medicine news etc Does a new research drug achieve a higher cure rate compared to existing treatments Design and conduct your own studies to investigate questions of interest Is chocolate beneficial to health How do states differ in the proportion of undergraduate students who engage in online gaming Engage critically with the information age by recognizing how data analysis transforms into meaningful insights raw information 6 Branches of Statistics STATISTICS Descriptive Statistics Inferential Statistics Organizing data Summarizing data Presenting data in an informative way Determining something about a population based on a sample Or methods for making decisions predictions and drawing conclusions about populations 7 Probability vs Statistical Inference Probability Inference 8 Example 1 Crime Analysis in Austin The City of Austin provides data on the date time and location of police reports On the right is a heat map showing the number of police reports in each ZIP code within Austin Question Is the heat map of crime frequency an example of descriptive or inferential statistics 9 Example 1 Crime Analysis in Austin Solution The City of Austin provides data on the date time and location of police reports On the right is a heat map showing the number of police reports in each ZIP code within Austin Question Is the heat map of crime frequency an example of descriptive or inferential statistics Answer Descriptive statistics 10 Example 2 Crime Analysis in Austin The City of Austin provides data on the date time and location of police reports In the plot on the right each dot represents the total number of police reports for a given day while the blue line shows the best fit trend in the average number of daily reports The part of the blue line that extends past the data is this model s attempt to predict the number of police reports in the future 2023 to 2025 Question Is the prediction portion of this plot descriptive or inferential statistics 11 Example 2 Crime Analysis in Austin Solution The City of Austin provides data on the date time and location of police reports In the plot on the right each dot represents the total number of police reports for a given day while the blue line shows the best fit trend in the average number of daily reports The part of the blue line that extends past the data is this model s attempt to predict the number of police reports in the future 2023 to 2025 Question Is the prediction portion of plot descriptive or inferential statistics this Answer Inferential statistics 12 Example 3 Sunflower Height Determine whether each of the following three statements is descriptive or inferential statistics 1 The average height of a random sample of sunflowers grown in East Texas was 140 centimeters 1 The average height of a random sample of sunflowers grown in West Texas was 134 centimeters 1 Therefore sunflowers grown in East Texas tend to be https pixabay com photos flowers sunflower petals flora 7135053 taller than those grown in West Texas 13 Example 3 Sunflower Height Solution Determine whether each of the following three statements is descriptive or inferential statistics 1 The average height of a random sample of sunflowers grown in East Texas was 140 centimeters Descriptive statistics This statement summarizes data collected from a specific sample 2 The average height of a random sample of sunflowers grown in West Texas was 134 centimeters Descriptive statistics This also summarizes data from a specific sample 3 Therefore sunflowers grown in East Texas tend to be taller than those grown in West Texas Inferential statistics This draws a conclusion about a larger population based on the sample data making it an inference https pixabay com photos flowers sunflower petals flora 7135053 14 Your Turn 1 Identify each of the following as either descriptive or inferential statistics 1 The average exam score on the STAT 302 final exam last semester was 89 1 Households with children under the age of 18 are more likely to have Internet access 77 compared to those without children 68 1 Sara who cuts and styles hair in her home salon had 25 customers last week 15 Your Turn 1 Solution 16 Statistics is all about data
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