Created by Tracy_Michaud Teacher Terms in this set (8) discrete number of large coffees sold at MacDonald's in 1 day discrete number of tires sold at VIP per week discrete number of sophomores in this class discrete number of Gatorade's sold out of the cafe machine each week continuous temperature in the classroom continuous You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Record the number of ones, twos, threes, fours, fives, and sixes you get in Table 1.7 and Table 1.8 (frequency is the number of times a particular face of the die occurs): Did the two experiments have the same results? The Pareto chart has the bars sorted from largest to smallest and is easier to read and interpret. For example, call-in surveys are invariably biased, because people choose to respond or not. Roll one fair die (six-sided) 20 times. Besides herself, Lisas group will consist of Marcierz, Cuningham, and Cuarismo. The weights of the soups ([latex]19[/latex] ounces, [latex]14.1[/latex] ounces, [latex]19[/latex] ounces) are quantitative continuous data because you measure weights as precisely as possible. If you count the number of phone calls you receive for each day of the week, you might get values such as zero, one, two, or three. Chapter 1: Discrete or Continuous? Flashcards | Quizlet The Literary Digest Poll, Virtual Laboratories in Probability and Statistics http://www.math.uah.edu/stat/data/LiteraryDigest.html (accessed May 1, 2013). The random variable X = the number of successes obtained in the n independent trials. feet, and 210 sq. Manufacturers regularly run tests to determine if the amount of beverage in a 16-ounce can falls within the desired range. List two reasons why the data may differ. Is this accurate? and you must attribute OpenStax. If you did the experiment a third time, do you expect the results to be identical to the first or second experiment? 1)At a college there are 120 freshmen, 90 sophomores, 110 juniors, and 80 seniors. We might make different choices of what we think is the best graph depending on the data and the context. Also try to identify additional data sets in this example. At the end of the term, the quiz scores are reported as A, B, C, D, or F. Work collaboratively to determine the correct data type (quantitative or qualitative). The sampling method was: Name the sampling method used in each of the following situations: convenienceclusterstratified systematicsimple random. If the survey is done well, the answer is yes. By using simple random sampling, select states to be part of the cluster. The weights (in pounds) of their backpacks are 6.2, 7, 6.8, 9.1, 4.3. Quantitative data are the result of counting or measuring attributes of a population. >. There is not enough information given to judge if either one is correct or incorrect. To choose a simple random sample of size three from the other members of her class, Lisa could put all 31 names in a hat, shake the hat, close her eyes, and pick out three names. quantitative continuous, 8.32 miles Each student is chosen using simple random sampling. Use the column numbers: one through six. Record the quiz scores that correspond to these numbers. That is, a member of the population may be chosen only once. For example, a computer software store conducts a marketing study by interviewing potential customers who happen to be in the store browsing through the available software. The chart in Figure 1.11(b) is organized by the size of each wedge, which makes it a more visually informative graph than the unsorted, alphabetical graph in Figure 1.11(a). Yes, there will most likely be a degree of variation between any two studies, even if they are set up and run the same way. Name data sets that are quantitative discrete, quantitative continuous, and qualitative. Random sampling methods include simple random sampling, stratified sampling, cluster sampling, and systematic sampling. Do you think that either of these samples is representative of (or is characteristic of) the entire 10,000 part-time student population? The data are the weights of backpacks with books in them. Quantitative data are the result of counting or measuring attributes of a population. Create a systematic sample of 12 quiz scores. In a college population of 10,000 people, suppose you want to pick a sample of As a class, determine whether or not the following samples are representative. A question on a survey reads: Do you prefer the delicious taste of Brand X or the taste of Brand Y? Is this a fair question? On your calculator, press Math and arrow over to PRB. The librarian has a tally sheet on which she marks whether books are checked out by an adult or a child. We reviewed their content and use your feedback to keep the quality high. No. The data he collects are summarized in the histogram. The data she collects are summarized in the pie chart [link]. Suppose an airline conducts a survey. If a registered voter answers the phone or is available to come to the phone, that registered voter is asked whom he or she intends to vote for and whether the debate changed his or her opinion of the candidates. the number of data values is increased), their sample results (the average amount of time a student sleeps) might be closer to the actual population average. Qualitative data are generally described by words or letters. Press ENTER. Would you expect the data to be identical? We cannot assume that crime rate impacts education level or that education level impacts crime rate. For example, families can have only a discrete number of children: 1, 2, 3, etc. Lowercase letters like What type of data is this? Possible lurking variables include police expenditures, unemployment levels, region, average age, and size. Press 5:randInt( and enter 1, 60). In this situation, create a bar graph and not a pie chart. Most data can be put into the following categories: Qualitative data are the result of categorizing or describing attributes of a population. This variability in samples cannot be stressed enough. But still, their samples would be, in all likelihood, different from each other. Now, suppose we take a third sample. Record the quiz scores that correspond to these numbers. In a pie chart, categories of data are represented by wedges in a circle and are proportional in size to the percent of individuals in each category. The seven It is better for the person conducting the survey to select the sample respondents. The colors red, black, black, green, and gray are qualitative data. Compute the number of ways to select 3 juniors from 6 as follows: Sample answer: The sample is not representative of the population of all college textbooks. Keep counting ten quiz scores and recording the quiz score until you have a sample of 12 quiz scores. Again, you sample the same five students. The mean, , and variance, 2, for the binomial probability distribution are. Sample Answer: Not all people have a listed phone number. Instructions: Use the Random Number Generator to pick samples. Figure 3. gym has 15 machines, one gym has ten machines, one gym has 22 machines, and the other gym has 20 Most of these students are, more than likely, paying more than the average part-time student for their books. What is the proportion of deaths between 2007 and 2012? Patients were asked to use the software program twice a day, once in the morning and once in the evening. As you become accustomed to sampling, the variability will begin to seem natural. (4.4.2) 2 = n p q. Doreen and Jung each take samples of 500 students. A high school principal polls 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors regarding policy changes for after school activities. The data are the number of machines in a gym. Who is correct? Do you think that this sample is representative of (or is characteristic of) the entire 20,000 listener population? Then stop the tenth person as they leave a different building on campus at 1:50 in the afternoon. To find the average annual income of all adults in the United States, sample U.S. congressmen. A political party wants to know the reaction of voters to a debate between the candidates. For example, the quiz scores for each student are recorded throughout the term. Notice that the frequencies do not add up to the total number of students. For column 1, Press 5:randInt( and enter 1,10). All data that are the result of measuring are quantitative continuous data assuming that we can measure accurately. The second sample is a group of senior citizens who are, more than likely, taking courses for health and interest. A medical researcher interviews every third cancer patient from a list of cancer patients at a local hospital. Make the description Use the following data to answer the next five exercises: Two researchers are gathering data on hours of video games played by school-aged children and young adults. The actual process of sampling causes sampling errors. Solved Question 34 - Which of the following is an example of - Chegg >. Discrete and Continuous Data - Math is Fun $150; Measuring angles in radians might result in such numbers as , and so on. They both did. The class boundaries are [latex]10[/latex] to less than [latex]13[/latex], [latex]13[/latex] to less than[latex]16[/latex],[latex]16[/latex] to less than[latex]19[/latex],[latex]19[/latex] to less than[latex]22[/latex], and [latex]22[/latex] to less than[latex]25[/latex]. Arrow over to PRB. Continuous data are often the results of measurements like lengths, weights, or times. Suppose Doreen and Jung both decide to study the average amount of time students at their college sleep each night. In polling, samples that are from 1,200 to 1,500 observations are considered large enough and good enough if the survey is random and is well done. Would the sample size be large enough if the population is school-aged children and young adults in the United States? a. These data take on only certain numerical values. Why? All students in those two years are in the sample. the number of data values is increased), their sample results (the average amount of time a student sleeps) might be closer to the actual population average. The quiz scores (20 of them) in these 2 columns are the cluster sample. You are going to use the random number generator to generate different types of samples from the data. Since these samples are not representative of the entire population, is it wise to use the results to describe the entire population? We choose ten different part-time students from the disciplines of chemistry, math, English, psychology, sociology, history, nursing, physical education, art, and early childhood development. No, this is a convenience sample taken from individuals who visited an exhibition in the Angeles Convention Center. Many of these students are taking first term calculus in addition to the organic chemistry class. Hair color, blood type, ethnic group, the car a person drives, and the street a person lives on are examples of qualitative data. Weights are quantitative continuous data. Use the column numbers: one through six. The first study was performed by the company that designed the software program. Long beach City is the seventh largest in California the college has an enrollment of approximately 27,000 students. Be aware that as you take data, your data may vary somewhat from the data someone else is taking for the same purpose. feet. For instance, hair color might be black, dark brown, light brown, blonde, gray, or red. Samples of only a few hundred observations, or even smaller, are sufficient for many purposes. The graph in [link] is a Pareto chart. 0.73381; In some situations, having small samples is unavoidable and can still be used to draw conclusions. This particular bar graph in Figure 1.9 can be difficult to understand visually. Americas Smithsonian., The job of the statistician is to see through the variability and draw appropriate conclusions. The size of a sample (often called the number of observations) is important. The data are the number of machines in a gym. From a group of 6 juniors and 5 sophomores a committee of 3 juniors and He has used a simple random sample method. This is true even when the samples are well-chosen and representative of the population. A student interviews classmates in his algebra class to determine how many pairs of jeans a student owns, on the average. Press ENTER 2 more times (even the repeats). The data are the colors of houses. In statistics, a sampling bias is created when a sample is collected from a population and some members of the population are not as likely to be chosen as others (remember, each member of the population should have an equally likely chance of being chosen). Try to identify additional data sets in this example. Does this change the validity of the conclusions from [link]? But graphs can be even more helpful in understanding the data. With the additional information, comment on how accurately you think the sample statistics reflect the population parameters. Any experiment that has characteristics two and three and where n = 1 is . The students spend the following amounts: c. The sample is unbiased, but a larger sample would be recommended to increase the likelihood that the sample will be close to representative of the population. Most statisticians use various methods of random sampling in an attempt to achieve this goal. But graphs can be even more helpful in understanding the data. Lecture 1. During the same year, George Gallup conducted his own poll of 30,000 prospective voters. For example, suppose Lisa wants to form a four-person study group (herself and three other people) from her pre-calculus class, which has 31 members not including Lisa. a. stratified; b. systematic; c. simple random; d. cluster; e. convenience. then you must include on every digital page view the following attribution: Use the information below to generate a citation. a. http://www.gallup.com/poll/146822/gallup-healthways-index-questions.aspx (accessed May 1, 2013). Earthquakes are quantified according to the amount of energy they produce (examples are 2.1, 5.0, 6.7). IQ scores (This may cause some discussion.). This would leave out many students who do not play games at all and skew the data. Hint: data that are discrete often start with the words "the number of." the number of pairs of shoes you own; the type of car you drive; the distance it is from your home to the nearest grocery store; the number of classes you take per school year; the type of calculator you use The data he collects are summarized in the histogram. As an Amazon Associate we earn from qualifying purchases. Quantitative data may be either discrete or continuous. You sample the same five students. Include in the report how the survey was conducted and why the results may not be accurate. With this additional information, do you feel that all demographic and ethnic groups were equally represented at the event? Any group of n individuals is equally likely to be chosen by any other group of n individuals if the simple random sampling technique is used. Determine if the variable is qualitative or quantitative. data. We need to evaluate the statistical studies we read about critically and analyze them before accepting the results of the studies. Is a sample of 500 volunteers a reliable measure for a population of 2,500? Think about what contributes to making Doreens and Jungs samples different. The first study collected the data in [link]. Test 1.docx - Test 1 1. Determine if the variable is - Course Hero During the past 30 days, for about how many days did poor health keep you from doing your usual activities? textbook in each subject. Both samples are biased. The random numbers 0.94360 and 0.99832 do not contain appropriate two digit numbers. Ask everyone to include their age then take a random sample from the data. Conducting the survey on a holiday weekend will not produce representative results. [link] contains the total number of deaths worldwide as a result of earthquakes from 2000 to 2012. The wording may influence responses. Divide your college faculty by department. A high school educational researcher interviews 50 high school female teachers and 50 high school male teachers. Notice that backpacks carrying three books can have different weights. A random survey was conducted of 3,274 people of the microprocessor generation (people born Quantitative data may be either discrete or continuous. [reveal-answer q=935468]Show Answer[/reveal-answer] [hidden-answer a=935468]This pie chart shows the students in each year, which is qualitative data. This is important to know when we think about what the data are telling us. Our choice also depends on what we are using the data for. Press ENTER two more times for the other 2 random numbers. Data, Sampling, and Variation in Data and Sampling by OpenStaxCollege is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted. Would this affect the data if students knew about the award before the study? Starting with that student, every 50th student is chosen until 75 students are included in the sample. First, we use convenience sampling and survey ten students from a first term organic chemistry class. Which of the potential problems with samples discussed in [link] could explain this connection? Record the number and the first quiz score. The amount of money they spend on books is probably much less than the average parttime student. The registrar at State University keeps records of the number of credit hours students complete each semester. Variation is present in any set of data. A study is done to determine the average tuition that San Jose State undergraduate students pay per semester. This is completely natural. If not, do you think the percents of the population are actually higher or lower than the sample statistics? >. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. $36; a. stratified; b. systematic; c. simple random; d. cluster; e. convenience. Factors not related to the sampling process cause nonsampling errors. The following graph is the same as the previous graph but the Other/Unknown percent (9.6%) has been included. No, even though the sample is a large portion of the population, two responses are not enough to justify any conclusions. >. Since these samples are not representative of the entire population, is it wise to use the results to describe the entire population? (ratio) The number of deaths in a defined time period (cannot have a The day after the debate, the partys polling staff calls 1,200 randomly selected phone numbers. However, for a biased sampling technique, even a large sample runs the risk of not being representative of the population. It also could not be used if the percentages added to less than 100%. Notice how much larger the percentage for part-time students at Foothill College is compared to De Anza College. Amount of money, pulse rate, weight, number of people living in your town, and number of students who take statistics are examples of quantitative data. [/hidden-answer], Determine the correct data type (quantitative or qualitative). Answers will vary. feet. 1.2: Data: Quantitative Data & Qualitative Data is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. Two graphs that are used to display qualitative data are pie charts and bar graphs. Which study is more reliable? A pie chart cannot be used. Record the number. Non-response or refusal of subject to participate: The collected responses may no longer be representative of the population. The freshman, sophomore, junior, and senior years are numbered one, two, three, and four, respectively. Besides simple random sampling, there are other forms of sampling that involve a chance process for getting the sample. The second sample is taken using a list of senior citizens who take P.E. feet, 190 sq. Data that are not only made up of counting numbers, but that may include fractions, decimals, or irrational numbers, are called quantitative continuous data. In the graph, the percentages add to more than 100% because students can be in more than one category. They both did. If you and your friends carry backpacks with books in them to school, the numbers of books in the backpacks are discrete data and the weights of the backpacks are continuous data. 22. value: 0.19 points Suppose that A is the set of sophomores at your school, B is the set of students in discrete mathematics at your school, and the universal set U is the set of all students at your school. The graph in Figure 3 is a Pareto chart. 0.51470; The distance it is from your home to the nearest grocery store. That's the intersection A\B. b. The data are the weights of backpacks with books in them. Number of new AIDS cases in CA in a year (counts) (ratio/interval) Years of school completed (ratio) The number of children in the family (cannot have a half a child!) The first 50 people who walk into a sporting event are polled on their television preferences. Suppose Doreen and Jung both decide to study the average amount of time students at their college sleep each night. At the end of the term, the quiz scores are reported as A, B, C, D, or F. Work collaboratively to determine the correct data type (quantitative or qualitative). >. Any group of n individuals is equally likely to be chosen as any other group of n individuals if the simple random sampling technique is used. Seven hundred and seventy-one distance learning students at Long Beach City College responded to surveys in the Self-selected samples: Responses only by people who choose to respond, such as call-in, Sample size issues: Samples that are too small may be unreliable. These data take on only certain numerical values. 0.14669; Compare the fractions 999/10,000 and 999/9,999. Hint: Data that are discrete often start with the words the number of.. There are many school-aged children and young adults in the United States, and the study was done at only one school, so the sample size is not large enough to reflect the population. If Doreen and Jung took larger samples (i.e. When properly selected, larger samples model the population more closely than smaller samples. Yes, the sample size of 150 would be large enough to reflect a population of one school. What type of data is that? There are no strict rules concerning which graphs to use. Asking all 10,000 students is an almost impossible task. Continuous Variable - Types, Examples and Discrete variables - BYJU'S That is, once a member is picked, that member goes back into the population and thus may be chosen more than once. We are interested in the average amount of money a part-time student spends on books in the fall term. Suppose that A is the set of sophomores at your school and B is the set of students in discrete math at your school. Collecting data carelessly can have devastating results. expanding the selection of subjects he investigates so that it is more representative of all subjects studied by college students, and, expanding the selection of textbooks he investigates within each subject to include a. Qualitative data are also often called categorical data. On your calculator, press Math and arrow over to PRB. Express each of these sets in terms of Aand B. a) the set of sophomores at your school who are not taking discrete mathematics, b) the set of students at your school who either are sophomores or are taking discrete mathematics, a)the set of sophomores at your school who are not taking discrete mathematics, b)the set of students at your school who either are sophomores or are taking discrete mathematics, Your email address will not be published. $53; The survey was conducted using six similar flights. As a rule, the larger the sample, the smaller the sampling error. Are these problems examples of sampling error or nonsampling error? Think about what contributes to making Doreens and Jungs samples different. The data may be skewed; however, the American Medical Association is not concerned with the success of the software and so should be objective. Non-response or refusal of subject to participate: The collected responses may no longer be representative of the population. Measurements of the amount of beverage in a 16-ounce can may vary because different people make the measurements or because the exact amount, 16 ounces of liquid, was not put into the cans.
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