Learning Objectives<\/h3>\n- Determine whether a value calculated from a group\u00a0is a statistic or a parameter<\/li>\n \t
- Identify the difference between a census and a sample<\/li>\n \t
- Identify the population of a study<\/li>\n \t
- Determine whether a measurement\u00a0is categorical or qualitative<\/li>\n<\/ul><\/div>\n
Populations and Samples<\/h2>\nSelecting A Focus<\/h3>\nBefore we begin gathering and analyzing data we need to characterize the population<\/strong> we are studying. If we want to study the amount of money spent on textbooks by a typical first-year college student, our population might be all first-year students at your college.\u00a0 Or it might be:\n- All first-year community college students in the state of Washington.<\/li>\n \t
- All first-year students at public colleges and universities in the state of Washington.<\/li>\n \t
- All first-year students at all colleges and universities in the state of Washington.<\/li>\n \t
- All first-year students at all colleges and universities in the entire United States.<\/li>\n \t
- And so on.<\/li>\n<\/ul>
![\"Black](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/165\/2017\/06\/13230541\/3020915387_22f5fb3e6d_z.jpg\")
<\/a>\n\nPopulation<\/h3>\n\n\nThe population<\/strong> of a study is the group the collected data is intended to describe.\n\n<\/div>\n<\/div>\nSometimes the intended population is called the target population<\/strong>, since if we design our study badly, the collected data might not actually be representative of the intended population.\n\nWhy is it important to specify the population? We might get different answers to our question as we vary the population we are studying. First-year students at the University of Washington might take slightly more diverse courses than those at your college, and some of these courses may require less popular textbooks that cost more; or, on the other hand, the University Bookstore might have a larger pool of used textbooks, reducing the cost of these books to the students. Whichever the case (and it is likely that some combination of\u00a0these and other factors are in play), the data we gather from your college will probably not be the same as that from the University of Washington. Particularly when conveying our results to others, we want to be clear about the population we are describing with our data.\n\nexample<\/h3>\nA newspaper website contains a poll asking people their opinion on a recent news article.\n\nWhat is the population?\n[reveal-answer q=\"330548\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"330548\"]While the target (intended) population may have been all people, the real population of the survey is readers of the website.[\/hidden-answer]\n\n<\/div>\n\n\nIf we were able to gather data on every member of our population, say the average (we will define \"average\" more carefully in a subsequent section) amount of money spent on textbooks by each first-year student at your college during the 2009-2010 academic year, the resulting number would be called a parameter<\/strong>.\n\n\n\nParameter<\/h3>\n<\/div>\n\n\nA parameter<\/strong> is a value (average, percentage, etc.) calculated using all the data from a population\n\n<\/div>\n<\/div>\n<\/div>\nWe seldom see parameters, however, since surveying an entire population is usually very time-consuming and expensive, unless the population is very small or we already have the data collected.\n\n\n\nCensus<\/h3>\n<\/div>\n\n\nA survey of an entire population is called a census<\/strong>.\n\n<\/div>\n<\/div>\n<\/div>\nYou are probably familiar with two common censuses: the official government Census that attempts to count the population of the U.S. every ten years, and voting, which asks the opinion of all eligible voters in a district. The first of these demonstrates one additional problem with a census: the difficulty in finding and getting participation from everyone in a large population, which can bias, or skew, the results.\n\nThere are occasionally times when a census is appropriate, usually when the population is fairly small. For example, if the manager of Starbucks wanted to know the average number of hours her employees worked last week, she should be able to pull up payroll records or ask each employee directly.\n\nSince surveying an entire population is often impractical, we usually select a sample<\/strong> to study.\n\n\n\nSample<\/h3>\n<\/div>\n\n\nA sample<\/strong> is a smaller subset of the entire population, ideally one that is fairly representative of the whole population.\n\n<\/div>\n<\/div>\n<\/div>\nWe will discuss sampling methods in greater detail in a later section.\u00a0 For now, let us assume that samples are chosen in an appropriate manner.\u00a0 If we survey a sample, say 100 first-year students at your college, and find the average amount of money spent by these students on textbooks, the resulting number is called a statistic<\/strong>.\n\n\n\nStatistic<\/h3>\n<\/div>\n\n\nA statistic<\/strong> is a value (average, percentage, etc.) calculated using the data from a sample.\n\n<\/div>\n<\/div>\n\nexample<\/h3>\nA researcher wanted to know how citizens of Tacoma felt about a voter initiative. To study this, she goes to the Tacoma Mall and randomly selects 500 shoppers and asks them their opinion. 60% indicate they are supportive of the initiative. What is the sample and population? Is the 60% value a parameter or a statistic?\n[reveal-answer q=\"55672\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"55672\"]\n\nThe sample is the 500 shoppers questioned. The population is less clear. While the intended population of this survey was Tacoma citizens, the effective population was mall shoppers. There is no reason to assume that the 500 shoppers questioned would be representative of all Tacoma citizens.\n\nThe 60% value was based on the sample, so it is a statistic.\n\n[\/hidden-answer]\n\nThe examples on this page are detailed in the following video.\n\nhttps:\/\/youtu.be\/NlcDpqnqBKY\n\n<\/div>\n\nTry It Now<\/h3>\nTo determine the average length of trout in a lake, researchers catch 20 fish and measure them. What is the sample and population in this study?\n[reveal-answer q=\"707088\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"707088\"]The sample is the 20 fish caught. The population is all fish in the lake. The sample may be somewhat unrepresentative of the population since not all fish may be large enough to catch the bait.[\/hidden-answer]\n\n\n\nA college reports that the average age of their students is 28 years old. Is this a statistic or a parameter?\n[reveal-answer q=\"564641\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"564641\"]This is a parameter, since the college would have access to data on all students (the population)[\/hidden-answer]\n\n\n<\/div>\n<\/div>\n<\/div>\nCategorizing Data<\/h2>\nQuantitative or Categorical<\/h3>\nOnce we have gathered data, we might wish to classify it.\u00a0 Roughly speaking, data can be classified as categorical data or quantitative data.\n\n![\"vertical](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/165\/2017\/06\/13230543\/12210424505_2da556e2df_z.jpg\")
<\/a>\n\n\n\nQuantitative and categorical data<\/h3>\n<\/div>\n\n\nCategorical (qualitative) data<\/strong> are pieces of information that allow us to classify the objects under investigation into various categories.\n\nQuantitative data<\/strong> are responses that are numerical in nature and with which we can perform meaningful arithmetic calculations.\n\n<\/div>\n<\/div>\n\nexample<\/h3>\nWe might conduct a survey to determine the name of the favorite movie that each person in a math class saw in a movie theater.\n\nWhen we conduct such a survey, the responses would look like: Finding Nemo<\/em>, The Hulk<\/em>, or Terminator 3: Rise of the Machines<\/em>. We might count the number of people who give each answer, but the answers themselves do not have any numerical values: we cannot perform computations with an answer like \"Finding Nemo<\/em>.\" Is this categorical or quantitative data?\n[reveal-answer q=\"914414\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"914414\"]This would be categorical data.[\/hidden-answer]\n\n<\/div>\n\nExample<\/h3>\nA survey could ask the number of movies you have seen in a movie theater in the past 12 months (0, 1, 2, 3, 4, . . .).\u00a0Is this categorical or quantitative data?\n[reveal-answer q=\"798578\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"798578\"]This would be quantitative data.Other examples of quantitative data would be the running time of the movie you saw most recently (104 minutes, 137 minutes, 104 minutes, . . .) or the amount of money you paid for a movie ticket the last time you went to a movie theater ($5.50, $7.75, $9, . . .).[\/hidden-answer]\n\n<\/div>\nSometimes, determining whether or not data is categorical or quantitative can be a bit trickier. \u00a0In the next example, teh data collected is in numerical form, but it is not quantitative data. \u00a0Read on to find out why.\n
Populations and Samples<\/h2>\nSelecting A Focus<\/h3>\nBefore we begin gathering and analyzing data we need to characterize the population<\/strong> we are studying. If we want to study the amount of money spent on textbooks by a typical first-year college student, our population might be all first-year students at your college.\u00a0 Or it might be:\n- All first-year community college students in the state of Washington.<\/li>\n \t
- All first-year students at public colleges and universities in the state of Washington.<\/li>\n \t
- All first-year students at all colleges and universities in the state of Washington.<\/li>\n \t
- All first-year students at all colleges and universities in the entire United States.<\/li>\n \t
- And so on.<\/li>\n<\/ul><\/a>\n\n
Population<\/h3>\n\n\nThe population<\/strong> of a study is the group the collected data is intended to describe.\n\n<\/div>\n<\/div>\nSometimes the intended population is called the target population<\/strong>, since if we design our study badly, the collected data might not actually be representative of the intended population.\n\nWhy is it important to specify the population? We might get different answers to our question as we vary the population we are studying. First-year students at the University of Washington might take slightly more diverse courses than those at your college, and some of these courses may require less popular textbooks that cost more; or, on the other hand, the University Bookstore might have a larger pool of used textbooks, reducing the cost of these books to the students. Whichever the case (and it is likely that some combination of\u00a0these and other factors are in play), the data we gather from your college will probably not be the same as that from the University of Washington. Particularly when conveying our results to others, we want to be clear about the population we are describing with our data.\n\nexample<\/h3>\nA newspaper website contains a poll asking people their opinion on a recent news article.\n\nWhat is the population?\n[reveal-answer q=\"330548\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"330548\"]While the target (intended) population may have been all people, the real population of the survey is readers of the website.[\/hidden-answer]\n\n<\/div>\n\n\nIf we were able to gather data on every member of our population, say the average (we will define \"average\" more carefully in a subsequent section) amount of money spent on textbooks by each first-year student at your college during the 2009-2010 academic year, the resulting number would be called a parameter<\/strong>.\n\n\n\nParameter<\/h3>\n<\/div>\n\n\nA parameter<\/strong> is a value (average, percentage, etc.) calculated using all the data from a population\n\n<\/div>\n<\/div>\n<\/div>\nWe seldom see parameters, however, since surveying an entire population is usually very time-consuming and expensive, unless the population is very small or we already have the data collected.\n\n\n\nCensus<\/h3>\n<\/div>\n\n\nA survey of an entire population is called a census<\/strong>.\n\n<\/div>\n<\/div>\n<\/div>\nYou are probably familiar with two common censuses: the official government Census that attempts to count the population of the U.S. every ten years, and voting, which asks the opinion of all eligible voters in a district. The first of these demonstrates one additional problem with a census: the difficulty in finding and getting participation from everyone in a large population, which can bias, or skew, the results.\n\nThere are occasionally times when a census is appropriate, usually when the population is fairly small. For example, if the manager of Starbucks wanted to know the average number of hours her employees worked last week, she should be able to pull up payroll records or ask each employee directly.\n\nSince surveying an entire population is often impractical, we usually select a sample<\/strong> to study.\n\n\n\nSample<\/h3>\n<\/div>\n\n\nA sample<\/strong> is a smaller subset of the entire population, ideally one that is fairly representative of the whole population.\n\n<\/div>\n<\/div>\n<\/div>\nWe will discuss sampling methods in greater detail in a later section.\u00a0 For now, let us assume that samples are chosen in an appropriate manner.\u00a0 If we survey a sample, say 100 first-year students at your college, and find the average amount of money spent by these students on textbooks, the resulting number is called a statistic<\/strong>.\n\n\n\nStatistic<\/h3>\n<\/div>\n\n\nA statistic<\/strong> is a value (average, percentage, etc.) calculated using the data from a sample.\n\n<\/div>\n<\/div>\n\nexample<\/h3>\nA researcher wanted to know how citizens of Tacoma felt about a voter initiative. To study this, she goes to the Tacoma Mall and randomly selects 500 shoppers and asks them their opinion. 60% indicate they are supportive of the initiative. What is the sample and population? Is the 60% value a parameter or a statistic?\n[reveal-answer q=\"55672\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"55672\"]\n\nThe sample is the 500 shoppers questioned. The population is less clear. While the intended population of this survey was Tacoma citizens, the effective population was mall shoppers. There is no reason to assume that the 500 shoppers questioned would be representative of all Tacoma citizens.\n\nThe 60% value was based on the sample, so it is a statistic.\n\n[\/hidden-answer]\n\nThe examples on this page are detailed in the following video.\n\nhttps:\/\/youtu.be\/NlcDpqnqBKY\n\n<\/div>\n\nTry It Now<\/h3>\nTo determine the average length of trout in a lake, researchers catch 20 fish and measure them. What is the sample and population in this study?\n[reveal-answer q=\"707088\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"707088\"]The sample is the 20 fish caught. The population is all fish in the lake. The sample may be somewhat unrepresentative of the population since not all fish may be large enough to catch the bait.[\/hidden-answer]\n\n\n\nA college reports that the average age of their students is 28 years old. Is this a statistic or a parameter?\n[reveal-answer q=\"564641\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"564641\"]This is a parameter, since the college would have access to data on all students (the population)[\/hidden-answer]\n\n\n<\/div>\n<\/div>\n<\/div>\nCategorizing Data<\/h2>\nQuantitative or Categorical<\/h3>\nOnce we have gathered data, we might wish to classify it.\u00a0 Roughly speaking, data can be classified as categorical data or quantitative data.\n\n<\/a>\n\n\n\nQuantitative and categorical data<\/h3>\n<\/div>\n\n\nCategorical (qualitative) data<\/strong> are pieces of information that allow us to classify the objects under investigation into various categories.\n\nQuantitative data<\/strong> are responses that are numerical in nature and with which we can perform meaningful arithmetic calculations.\n\n<\/div>\n<\/div>\n\nexample<\/h3>\nWe might conduct a survey to determine the name of the favorite movie that each person in a math class saw in a movie theater.\n\nWhen we conduct such a survey, the responses would look like: Finding Nemo<\/em>, The Hulk<\/em>, or Terminator 3: Rise of the Machines<\/em>. We might count the number of people who give each answer, but the answers themselves do not have any numerical values: we cannot perform computations with an answer like \"Finding Nemo<\/em>.\" Is this categorical or quantitative data?\n[reveal-answer q=\"914414\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"914414\"]This would be categorical data.[\/hidden-answer]\n\n<\/div>\n\nExample<\/h3>\nA survey could ask the number of movies you have seen in a movie theater in the past 12 months (0, 1, 2, 3, 4, . . .).\u00a0Is this categorical or quantitative data?\n[reveal-answer q=\"798578\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"798578\"]This would be quantitative data.Other examples of quantitative data would be the running time of the movie you saw most recently (104 minutes, 137 minutes, 104 minutes, . . .) or the amount of money you paid for a movie ticket the last time you went to a movie theater ($5.50, $7.75, $9, . . .).[\/hidden-answer]\n\n<\/div>\nSometimes, determining whether or not data is categorical or quantitative can be a bit trickier. \u00a0In the next example, teh data collected is in numerical form, but it is not quantitative data. \u00a0Read on to find out why.\n
- All first-year community college students in the state of Washington.<\/li>\n \t
- All first-year students at public colleges and universities in the state of Washington.<\/li>\n \t
- All first-year students at all colleges and universities in the state of Washington.<\/li>\n \t
- All first-year students at all colleges and universities in the entire United States.<\/li>\n \t
- And so on.<\/li>\n<\/ul><\/a>\n\n
Population<\/h3>\n
\n\nThe population<\/strong> of a study is the group the collected data is intended to describe.\n\n<\/div>\n<\/div>\nSometimes the intended population is called the target population<\/strong>, since if we design our study badly, the collected data might not actually be representative of the intended population.\n\nWhy is it important to specify the population? We might get different answers to our question as we vary the population we are studying. First-year students at the University of Washington might take slightly more diverse courses than those at your college, and some of these courses may require less popular textbooks that cost more; or, on the other hand, the University Bookstore might have a larger pool of used textbooks, reducing the cost of these books to the students. Whichever the case (and it is likely that some combination of\u00a0these and other factors are in play), the data we gather from your college will probably not be the same as that from the University of Washington. Particularly when conveying our results to others, we want to be clear about the population we are describing with our data.\n\nexample<\/h3>\nA newspaper website contains a poll asking people their opinion on a recent news article.\n\nWhat is the population?\n[reveal-answer q=\"330548\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"330548\"]While the target (intended) population may have been all people, the real population of the survey is readers of the website.[\/hidden-answer]\n\n<\/div>\n
\n\nIf we were able to gather data on every member of our population, say the average (we will define \"average\" more carefully in a subsequent section) amount of money spent on textbooks by each first-year student at your college during the 2009-2010 academic year, the resulting number would be called a parameter<\/strong>.\n\n\n\nParameter<\/h3>\n<\/div>\n
\n\nA parameter<\/strong> is a value (average, percentage, etc.) calculated using all the data from a population\n\n<\/div>\n<\/div>\n<\/div>\nWe seldom see parameters, however, since surveying an entire population is usually very time-consuming and expensive, unless the population is very small or we already have the data collected.\n\n\n\nCensus<\/h3>\n<\/div>\n
\n\nA survey of an entire population is called a census<\/strong>.\n\n<\/div>\n<\/div>\n<\/div>\nYou are probably familiar with two common censuses: the official government Census that attempts to count the population of the U.S. every ten years, and voting, which asks the opinion of all eligible voters in a district. The first of these demonstrates one additional problem with a census: the difficulty in finding and getting participation from everyone in a large population, which can bias, or skew, the results.\n\nThere are occasionally times when a census is appropriate, usually when the population is fairly small. For example, if the manager of Starbucks wanted to know the average number of hours her employees worked last week, she should be able to pull up payroll records or ask each employee directly.\n\nSince surveying an entire population is often impractical, we usually select a sample<\/strong> to study.\n\n\n\nSample<\/h3>\n<\/div>\n
\n\nA sample<\/strong> is a smaller subset of the entire population, ideally one that is fairly representative of the whole population.\n\n<\/div>\n<\/div>\n<\/div>\nWe will discuss sampling methods in greater detail in a later section.\u00a0 For now, let us assume that samples are chosen in an appropriate manner.\u00a0 If we survey a sample, say 100 first-year students at your college, and find the average amount of money spent by these students on textbooks, the resulting number is called a statistic<\/strong>.\n\n\n\nStatistic<\/h3>\n<\/div>\n
\n\nA statistic<\/strong> is a value (average, percentage, etc.) calculated using the data from a sample.\n\n<\/div>\n<\/div>\n\nexample<\/h3>\nA researcher wanted to know how citizens of Tacoma felt about a voter initiative. To study this, she goes to the Tacoma Mall and randomly selects 500 shoppers and asks them their opinion. 60% indicate they are supportive of the initiative. What is the sample and population? Is the 60% value a parameter or a statistic?\n[reveal-answer q=\"55672\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"55672\"]\n\nThe sample is the 500 shoppers questioned. The population is less clear. While the intended population of this survey was Tacoma citizens, the effective population was mall shoppers. There is no reason to assume that the 500 shoppers questioned would be representative of all Tacoma citizens.\n\nThe 60% value was based on the sample, so it is a statistic.\n\n[\/hidden-answer]\n\nThe examples on this page are detailed in the following video.\n\nhttps:\/\/youtu.be\/NlcDpqnqBKY\n\n<\/div>\n
\nTry It Now<\/h3>\nTo determine the average length of trout in a lake, researchers catch 20 fish and measure them. What is the sample and population in this study?\n[reveal-answer q=\"707088\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"707088\"]The sample is the 20 fish caught. The population is all fish in the lake. The sample may be somewhat unrepresentative of the population since not all fish may be large enough to catch the bait.[\/hidden-answer]\n\n\n\nA college reports that the average age of their students is 28 years old. Is this a statistic or a parameter?\n[reveal-answer q=\"564641\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"564641\"]This is a parameter, since the college would have access to data on all students (the population)[\/hidden-answer]\n\n\n<\/div>\n<\/div>\n<\/div>\n
Categorizing Data<\/h2>\n
Quantitative or Categorical<\/h3>\nOnce we have gathered data, we might wish to classify it.\u00a0 Roughly speaking, data can be classified as categorical data or quantitative data.\n\n
<\/a>\n\n\n\nQuantitative and categorical data<\/h3>\n<\/div>\n
\n\nCategorical (qualitative) data<\/strong> are pieces of information that allow us to classify the objects under investigation into various categories.\n\nQuantitative data<\/strong> are responses that are numerical in nature and with which we can perform meaningful arithmetic calculations.\n\n<\/div>\n<\/div>\n\nexample<\/h3>\nWe might conduct a survey to determine the name of the favorite movie that each person in a math class saw in a movie theater.\n\nWhen we conduct such a survey, the responses would look like: Finding Nemo<\/em>, The Hulk<\/em>, or Terminator 3: Rise of the Machines<\/em>. We might count the number of people who give each answer, but the answers themselves do not have any numerical values: we cannot perform computations with an answer like \"Finding Nemo<\/em>.\" Is this categorical or quantitative data?\n[reveal-answer q=\"914414\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"914414\"]This would be categorical data.[\/hidden-answer]\n\n<\/div>\n
\nExample<\/h3>\nA survey could ask the number of movies you have seen in a movie theater in the past 12 months (0, 1, 2, 3, 4, . . .).\u00a0Is this categorical or quantitative data?\n[reveal-answer q=\"798578\"]Show Answer[\/reveal-answer]\n[hidden-answer a=\"798578\"]This would be quantitative data.Other examples of quantitative data would be the running time of the movie you saw most recently (104 minutes, 137 minutes, 104 minutes, . . .) or the amount of money you paid for a movie ticket the last time you went to a movie theater ($5.50, $7.75, $9, . . .).[\/hidden-answer]\n\n<\/div>\nSometimes, determining whether or not data is categorical or quantitative can be a bit trickier. \u00a0In the next example, teh data collected is in numerical form, but it is not quantitative data. \u00a0Read on to find out why.\n
![\"Black](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/29213125\/3020915387_22f5fb3e6d_z.jpg\")
<\/a>\n