8.6: Quantway Core 2.7 Workforce (IT) - Student Lesson (2024)

INTRODUCTION

SPECIFIC OBJECTIVES

By the end of this collaboration, you should understand that

• each statistic—the mean, median, and mode—is a different summary of numerical data.
• conclusions derived from statistical summaries are subject to error.
• measures of central tendency can be used to make decisions.

By the end of this collaboration, you should be able to

• make good decisions using information about data.
• interpret the mean, median, or mode in terms of the context of the problem.
• match data sets with appropriate statistics.

SPECIFIC LANGUAGE AND LITERACY OBJECTIVES

By the end of this collaboration, you should be able to

• read and comprehend the problem situation.
• complete annotation and summarization with quantitative and information technology information from the problem situation.
• demonstrate an understanding of mathematics by writing complete and correct responses to questions.
• demonstrate ability to describe, analyze, and synthesize information using measures of central tendency to look at patterns of data.
• use appropriate quantitative and information technology vocabulary to discuss mathematics in this collaboration.

PROBLEM SITUATION: HOW DO STUDENTS TEXT?

You are the Director of Information Technology at White Oak Community College (WOCC). Recently, students and faculty have been complaining to you about the online campus platform. It can be difficult to communicate about assignments and school events on the platform.

Most students at WOCC do not have laptops or computers at home. Instead they use smartphones or tablets to do school work. Students also complain that it takes instructors too long to answer messages about homework assignments. Instructors complain that students do not check their messages often enough, or do not receive information about course work.

The college has a group of staff members who talk about technology issues on campus. This group is called the Committee for Virtual Learning (the Committee). The Committee proposes to install a mass text messaging system on campus. You believe that this is a good idea. This system is called EducText. The system would allow students and faculty to text about assignments, course work, and anything school-related for free. It would help instructors provide quick responses to students, and send text messages to the entire class at one time. EducText would allow the school to communicate time-sensitive information, using text messages, to students and staff about urgent safety issues, school closings, and weather alerts.

EducText is a very expensive system. Given the significant costs of implementing EducText, the Committee needs to decide if it is cost-effective. The Committee determines that implementation is only cost-effective if most students send or receive text messages at least 20 times a day. You assume that most students are active texters, but you must conduct research to understand how students at WOCC use text messaging in their daily lives. This will help you determine if EducText is worth the cost. You conduct this research during the 2014–2015 school year.

(1) Please answer, in one to two sentences, the following questions about the problem situation.

(a) What problem are the White Oak Community College faculty and students trying to solve?

(b) EducText would allow students and faculty to text about assignments, course work, and anything school related for free. Why is this important to the faculty and/or students?

(c) Why is it important for the Committee to know whether the students send or receive at least 20 text messages each day?

Now, let’s collect data about how often students in this class send or receive text messages.

(2) (a) What is the typical number of texts that students in this class send and receive each day? Discuss with your group the best way to approach this question. Try to find a number. Think about how you got that number.

(b) Based on the results of your class, would it be worth buying EducText at WOCC? Should the college purchase EducText?

Figure 1 below shows national data about the number of texts adults send and receive. These results are organized by age group.

Figure 1: Number of Texts Sent/Received Per Day, by Age Group in the U.S. during 2011²

(3) (a) Examine Figure 1. Be sure to read the labels in the figure carefully. Write at least two factually precise statements about the data. That is, write two statements that are based on information that is in the data chart above. Write your answer in 1–2 complete sentences. (It is important to write complete sentences because it helps your instructor better understand your mathematical thinking.) Be sure your answer is precise and complete.

Writing Tip! Writing precise and complete answers in complete sentences can be challenging. Here is an example of a possible answer to this question: Twenty-five to thirty-four year-old adults in the U.S. send or receive an average of 41.8 texts per day and a median of 20 texts per day.

(b) Now, use Figure 1 to draw one conclusion about texting and age. Write your answer in 1–2 complete sentences.

(c) If the texting data shown in Figure 1 for 18–24 year olds is representative of the texting habits of WOCC’s students, would the EducText system be worth the expense?

(4) Why do you think the mean number of texts sent and received is significantly greater than the median? Again, write your answer in 1–2 complete sentences.

(5) Figure 1 shows that, for 45–54 year olds, the mean number of texts is 14 and the median is 6. Construct a sample of six individuals to illustrate what a data set might look like that has a mean of 14 and median of 6. As you are working, think about the process you use to determine this set of numbers.

(6) What will generally be true for a data set with a significantly greater mean than median?

(7) Write an example set of five data points for which the mean is significantly less than the median.

(8) In your research, you decided to learn more about different uses of information technology. You wanted to understand the possible options that might be available for staff and students to communicate at White Oak Community College. You found the following statistics. In each case. decide whether the mean, median, mode is being used. If the statistic is not the mean, median, or mode, select “none.” Circle your answer.

i. Approximately half of all Americans between 18 and 24 send and receive at least 50 texts a day.

mean median mode none

ii. On average, American 18–29 year-olds send fifty more texts per day than 30–49 year-olds.

mean median mode none

iii. The best hour of the day to post on Twitter (measured by re-tweets) is at 5 p.m.

mean median mode none

iv. The average amount of time spent per Facebook visit is 20 minutes.

mean median mode none

v. 49% of 18–24-year-olds check Facebook when they wake up.

mean median mode none

vi. Among all social media sites, Facebook has the most users.

mean median mode none

vii. The average Facebook user is 40.5 years old.

mean median mode none

viii. Half of all Facebook users ages 18–29 have at least 300 Facebook friends.

mean median mode none

FURTHER APPLICATIONS

MAKING CONNECTIONS

Record the important mathematical ideas from the discussion.

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² http://www.pewinternet.org/2011/09/19/how-americans-use-text-messaging/