This module explains how objects can be counted mathematically and used to calculate probabilities. This helps us to tackle two of the objectives for this class:
Apply the basic rules of counting: fundamental counting principle, permutations, and combinations to solve problems.
Apply basic rules of probability including compound events, conditional probability, and expected value to solve problems.
Techniques from this chapter can be used to determine how many ways there are to roll a total of 7 or 11 on a pair of die or how many ways there are to pick lottery numbers.
Once we understand this process, we will use this information to determine how likely it is to roll 7 or 11 or win the lottery.
In this chapter, you will be introduced to statistics. This branch of mathematics is concerned with data – how it is collected, organized, analyzed, interpreted, and presented. Statistics is used in almost every occupation is some way.
In the health professions, data is collected and analyzed to determine whether a drug therapy is effective. In business, statistics are used to help understand consumer behavior and to create marketing campaigns based on that behavior. Engineers collect statistics to help them design better production systems. Cities and towns collect data on traffic patterns so that signals may be synchronized to make traffic flow better.
Calculate and interpret graphical and numerical summaries of data including measures of central tendency and dispersion.
Use the basic properties of the normal distribution to solve applied problems.
The sections below will help you to accomplish these goals by introducing the vocabulary and mathematical techniques needed to analyze data. Each of the section below contain a workbook and videos to help you master the content. Work out the practice problems in the workbook so that you have a record of your learning and can use them to study for quizzes and exams.
This sections begins a chapter on statistics. Statistics is a branch of mathematics concerned with how data is collected, organized, analyzed, interpreted, and presented. You will get a taste of each of these areas in the six sections in this chapter.
To begin, you need to understand what data is and where we get it from. Data can take many forms and are collected to help people understand problems in business and science. You may be familiar with the United States census that is conducted every ten years. In this census, the population of the United States answers questions about many topics. The data collected helps to apportion the United States Congress and allocate government spending.
Data is collected from users on the Internet to help companies understand consumers and market products to consumers. Studies are conducted by researchers to collect data on the efficacy of medical treatments and drugs. Even your college collects data on students to help them improve teaching and develop programs that help students to complete degrees.
The purpose of this section is to recognize the terminology used in statistical studies. We will do this through a series of questions that will help you to
distinguish qualitative data from quantitative data,
distinguish a population from a sample,
distinguish a statistic from a parameter,
and distinguish discrete data from continuous data.
The workbook and videos below are designed to help you accomplish these objectives. The workbook presents a brief outline of the topics followed by guided examples and practice problems. As you read through the guided examples, complete the accompanying practice problem next to it. This practice will help you to learn the information and embed it in your long term memory.
This content is created under Creative Commons license. You are free to use it commercially or non-commercially. You may also modify it. You can find the Word files on the College Mathematics Resources page.
This content was created by David Graser, Andrea Schaben and Shane Gibson of Yavapai College. Parts of the work were taken from the OER materials below:
Hintzmann, Linda, Pasadena Community College
Inigo, Maxie, Jameson, Jennifer, Kozak, Kate, Lanzetta, Maya, and Sonier, Kim; “College Mathematics for Everyday Life”, 2nd Edition
Lippman, David, “Math in Society”, 2.5 edition, 2017
When working with a model, you need to pay careful attention to the units on each variable.
Problems 1 The number y (in millions) of women in the workforce is given by the function $latex \displaystyle y=0.006{{x}^{2}}-0.018x+5.607$ where x is the number of years after 1900.
a. Find the value of y when x = 44. Explain what this means.
b. Use the model to find the number of women in the workforce in 2010.
The solution above is the correct strategy, but there is an error…can you find the error?
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