Lesson 1
Measures of Central Tendency
High School Algebra 1
Quiz
Strategies:
Structured Notes
Sample
Before Reading
I. Motivation
Scientists, marketing experts, political experts, and many other professionals perform research projects. For these projects, a hypothesis must be made and proven true or false. The data from these projects is then presented in books, newspapers, and magazines that students might read. The students will learn how to use central measures of tendency. The students will then find the central measures of tendency regarding their data.
"Scientists, marketing experts, political experts, and many other professionals perform research projects. When performing research projects, a hypothesis must be made and then tested to be proven true or false. You have done this. You selected a topic and formed a hypothesis. You then surveyed or tested your peers to collect data. This data then helped you prove your hypothesis true or false. The data that researchers collect is then presented in book, newspapers, and magazines for the public to read. We will be doing the same thing. Your data will be published in your report that is due on Friday. In order to present your data you are going to need to find its central measures of tendency. Today we will be looking at how to do this. Then you will find the central measures of tendency regarding your data."
II. Prior Knowledge
Students will understand how to perform a research project because they just finished a unit in science on research. We started our projects at the beginning of the unit. Students have already given out the surveys and have the data.
"First we need to find out what you all already know on this topic. To do this we are going to take a short warm-up. Take our your math notebooks, and copy down the four following problems off the overhead. Please show all of your work, and do not talk."
To find out exactly what students understand on the measures of central tendency they will be given a quick warm up which will be on a transparency:
1. Arrange each set of numbers in order from least to greatest
7, 19, 1, 14, 4, 9, 15, 5
______________________________________ 2. Arrange each set of numbers in order from lease to greatest
1.1, 0.25, 7.8, 2.5, 11.1, 0.5
______________________________________ 3. Find the difference
9,2 - 5.8
______________________________________ 4. Find the difference
16 - 5.1
______________________________________ Answers:
1. 1, 4, 5, 7, 9, 14, 15, 192. 0.25, 0.5, 1.1, 2.5, 7.8, 11.1
3. 3.4
4. 10.9
"Time is up, please stop working on the problems, and listen as I read off the answers. Correct your own work. The answer to number one is 1, 4, 5, 7, 9, 14, 15, 19. The answer to number two is 0.25, 0.5, 1.1, 2.5, 7.8, 11.1. The answer to number three is 3.4. The answer to number four is 10.9. Are there any questions on how we found those answers?"
"How did you find the answer to number 3?"
"Great question Ben, would someone like to share how they found the answer for number 3? Yes, Rachel."
"I wrote down 9.2, and directly under it placed 5.8. I then subtracted the two numbers. I had to cross out the 9 and replace it with 8, turning the 2 into 12. Then I got 4. I then subtracted 5 from 8, and got three. So my final answer is 3.4."
"Very good Rachel, that is exactly right. Are there any other questions?" After scanning the room, I see there are no more questions. "Please raise your hand is you got all four of the questions correct. Good, Please raise your hand if you got three of the four correct. Great."
After taking this quiz, the teacher will be able to assess what the students understand. In order to work with measures of central tendency, students need to understand how to place numbers in order from least to greatest. I predict the students will understand how to do these two skills. After a short discussion with the students though, I believe they will only understand mean and not the other types that we will be focusing on.
"When I say central measures of tendency, what do I mean?"
"Central measures of tendency are ways to describe data."
"Very good. How do I compute the mean?"
"To find the mean, you add all of the values together and divide by the number of values."
"Nice work. How do I compute the median?" After a scan of the classroom, it is apparent that none of the students knows how to compute the median. "Can anyone tell me how to compute the mode?" Again, no hands are raised. "How would I find the range?"
"Isn't it the just the largest number in the set of data?"
"Close but not quite. We will go over exactly how to find the range later. Can anyone tell me what a frequency table is? Or how I would make one?" Once again after scanning the classroom, none of the students has raised their hands.
III. Purpose
"Today you are all going to leave class knowing how to find the mean, median, mode, and range. You will also know what a frequency table is and how to make one. You will then be able to take this newfound information and apply it to your research paper. Today you are going to reading a text structured for description to be able to perform a task."
IV. Explicit/strategy instructions
Structured Notes (Cornell Notes)
Purpose
Provide students with a graphic organizer in which to take notes. Then present steps on how to take notes. Helps students determine what to include in their notes and increases students retention on the information."To help us achieve our purpose today, we need a good system for taking notes. This system will keep us organized. The system we will be learning today is Cornell Notes. It will help us determine what to include in our notes. The Cornell Note system will help you all retain information better, which will help for the up coming test on Friday."
Steps
Prepare paper by folding it at the pink line on left side, or providing students Cornell template. Record key points from lecture and reading. Form questions in the right hand column based off notes. These questions can help to clarify meanings and strengthen memory. Recite key words, answer questions, basic general ideas of notes. Reflect- Ask why is this significant to me? How do the notes fit with what I already know? How can I apply them? Review 10 minutes every week to increase retention. Summarize the main ideas learned.Steps
1. Prepare Paper
2. Record key points from lecture and reading
3. Form questions based off notes
4. Recite key words and answer questions
5. Reflect on notes
6. Review notes for 10 minutes
7. Summarize main ideas learned
"I want you all to take out your notebooks. To use Cornell Notes we first need to set up our paper. I want you all to fold the paper at the pink line on the left side. Across the top of the paper, write the title of your notes. In our case, we can use section 4.4. When using Cornell Notes, you are going to put the key points or terms on the left side. The key points and terms can come from lecture or reading. Then on the right side, put the information you will need or the definition of the terms. On the right side, you are also going to put examples and questions you form. These questions should help to clarify meanings and strengthen memory. After taking notes, recite key words, answer questions, and give basic general ideas of notes. We will start by practicing this with a partner; however, eventually you will be doing this on your own. You also need to reflect on your notes. This will include thinking about how they are significant to you, how they fit with what you already know, and how you can apply the notes. You will want to review ten minutes each week to increase retention. At the bottom of your notes is a section to write a summary. Here you will summarize what you have learned."
Model
We will practice with the first paragraph on descriptive statistics.
"Please open your books to section 4.4 on page 186. The first paragraph is on Descriptive Statistics. We will use this paragraph to understand how to take notes using Cornell Notes. We all have the paper set up. For the purpose of this example, my title will be Descriptive Statistics. You will continue the rest of your notes for 4.4 on this same sheet so you can use section 4.4 as a title if you would like. Please read to yourself the first paragraph."
Alternate Text with readability of 7.9
Descriptive Statistics
Statistics help us understand and describe raw data. The mean, median, and mode of a data set each tell us something about the central tendency of the data. From the central tendencies of data, we can see how the data tends to cluster around a value. The range provides information about the spread of the data.
"I thought statistics and central tendency were important key terms. I placed those terms on the left hand side. Then I put the definitions or any key information about these terms on the right side. Then I wrote a question I had after reading the paragraph. I also answered the question, which will be helpful when I am studying. Next, I wrote a short summary over the paragraph. My summary is on the bottom of the page in the summary section. I changed the color of the font so the summary would stand out. Are there any questions on how to use the Cornell Note taking system?"
"What happens if I run out of room on one sheet of paper?"
"Then you flip the sheet over and set it up the same way. If you do not like using the backside of a sheet of paper, then you just need to get a new sheet of paper, and set it up just as I have demonstrated. Are there any other questions?" No hands are raised. If more questions arise, they will be answered immediately.
Guided Practice
"Now please turn to page 188. Read the paragraph under the heading Frequency Tables. I want you all to take notes using the Cornell Note taking system on this paragraph. Raise your hand if you have any questions. We will be going over this paragraph as a class."
Alternate Text with readability of 7.7
Frequency Tables
A method for displaying data in which tally marks are used to show how often each element of the set occurs is a frequency table. Using this method, one does not need to list each occurrence of a number; instead, a tally mark is placed next to the number each time it occurs.
"Can someone please raise their hand and tell me what key terms or ideas you placed on the left side of your paper."
"I put the word Frequency table"
"Good job Randy, and what did you put on the right side of your paper next to frequency table?"
"I put it is a method of displaying data in which tally marks are used to show how often each element of the set occurs. I also put that with a frequency table you do not have to list each occurrence, instead you can place a tally mark next to the number each time it occurs."
"Wonderful, that is exactly right Randy. Did anyone have something else or something different in their notes?"
"No, I had exactly what Randy had."
"Alright students, from our work with Cornell Notes, it seems to me that you all understand how to do them. Are there any other questions before we move on?" No one responds.
During Reading
Schultz, J., Kennedy, P., Ellis, W., & Hollowell, K. (2003). Algebra
I. Austin: Holt, Rinehart and Winston.
Readability: 6.8 grade level using the Flesch-Kincaid; which is rather low for high school students. All of the vocabulary for the lesson is included in the text. I thought this would bring up the readability, however the definitions for these words are simplified and help to decrease the rating. By changing the words Explain to Elucidate and Show to Demonstrate the readability was increased to 7.5. The drawbacks of using a readability formula are well documented, so the cuing system and other readability factors should be considered. For this text, there are no pictures in the text that would help the reader, however, bold letters and different colored boxes help to set the text apart. This would decrease the readability of the text. The semantics and schematic would work best for someone who has some knowledge of math and statistics. Given that this section falls in the middle of a chapter, the students would have the necessary knowledge to understand the information. This decreases the readability. The syntax of the reading follows the same pattern as the rest of the book. The students would be accustom to this layout, which would also decrease the readability. The text structure from this section provides information on the measures of central tendency and vocabulary words with definitions. This would also decrease the readability. Overall, this section would work well for students reading below their grade level or who struggle with English. This text also would be beneficial for students who struggle with reading for the purpose of gaining knowledge. It would allow students to focus on the information that is being presented without worrying about how difficult the reading is.
For students who need a text at a higher level, an adapted text will be provided. Before each new chapter, these students will be provided with a packet, containing the adapted text. When the students are told to read from their textbook, these students will just need to open their packet and find the heading under which the reading is on. For this lesson, the adapted text comes from two sources. To insure all students are receiving the same information and will be able to participate in discussions, I adapted the paragraphs on frequency tables and descriptive statistics. The section on central measures of tendency are taken from: Benson, J., Dodge, S., Dodge, W., Hamberg, C., Milauskas, G., & Rukin, R. (1991). Algebra I: An integrated approach. Evanston: McDougal, Littell, and Company.
V. Text Structure
Expository – with a text structure of description, since the reading describes how to find the central tendencies and how to make a frequency table. The reading also includes five vocabulary words and their definitions within the text.
VI. Vocabulary
"Now we are going to look at the remaining vocabulary words we will need to understand the lesson. Please add these words and definitions to your Cornell Note sheets."
The words, definitions, and sentences will be written on the board before the start of class. The students will just need to copy down the words, definitions, and sentences into their notes.
Mean – of a data set is the quotient when the total number of elements divides the sum of all of the elements.
Sentence – The mean is the average data point in a set of data.
Median – of a data set is the middle number in the set when the elements are placed in numerical order. If there is an even number of elements, the median is the average of the two middle numbers.
Sentence – The median is the number in the middle of a data set.
Mode – of a data set is the element, if any that occurs most often. There may be no mode, one mode, or several modes.
Sentence – The mode is the number that occurs most often.
Range – of a data set is the difference between the greatest and least values in the set.
Sentence - The range tells us how large our set of data is.Frequency Table - A method of displaying data in which tally marks are used to show how often each element of the set occurs. Sentence - A frequency table allows us to visualize how many times each element occurred in a set of data.
VII. Content
"I now want all of you to finish reading section 4.4. Read from page186 through 189. Pay close attention to words that are highlighted, or italicized. If something is confusing to you, go back and reread the challenging material. Also, read the examples included in the textbook. We will be working through them as a class, but it will help if you have read them. Once you have read the section, please finish taking notes using the Cornell Note system. You all need to find the key points and terms to put into your notes. Write questions based off your notes. It will be your responsibility to recite, reflect, and review the information. Remember we have a test on Friday so it is important that you use the notes to help you prepare."
Alternate text with readability of 8.3
Measures of Central Tendency
Data analysis often involves finding quantities that represent the data. The mean, mode, and median are three such quantities. They are called measures of central tendency because they are ways to describe the center of a set of data.
The data below represents the number of boxes of grapefruit sold by 15 jazz-band members as part of a school fund-raiser.
We organize the data from smallest to largest.
The principle asked the band director to find the average number of boxes sold. The band director calculated the total number of boxes sold was 178. She then divided by 15 (the number of jazz-band members) to find the average number of boxes sold per member.
Total number of boxes sold = 178 = 11.9
Number of jazz-band members 15The average obtained by dividing the sum of a set of terms by the number of terms is called the mean of the data.
The band director noticed that the number 4 occurred among the data the greatest number of times. The number that occurs the greatest number of times is called the mode of the data.
The band director could have given a third type of average for the data by choosing the number 11. This number is the middle number of the data and is called the median. Since the total number of data values is an odd number, there are as many values greater than the median as there are values less than the median. When there is an even number of data values, the median is defined to be the mean of the two middle numbers.
Benson, J., Dodge, S., Dodge, W., Hamberg, C., Milauskas, G., & Rukin, R. (1991). Algebra I: An integrated approach. Evanston: McDougal, Littell, and Company.
"Now that you have all read through the text, we will look at the examples. Please add these examples to the right side of your Cornell Notes, and be sure to show work. Your notes should be labeled so you will be able to understand what has happened in each step. Place the label on the left side of your notes."
Example 1:
Find the mean, median, mode, and range of the batting average for five National League players: 0.372, 0.366, 0.362, 0.333, and 0.327.
Solution:"What is the mean of these five batting averages?"
"The mean is 0.352"
"Great job Amy. Can anyone tell me how Amy found the answer to be 0.352?"
"She added the five batting averages and then divided the sum by 5."
"Wonderful Tommy. Are there any questions on the mean?" No one raised their hand, so we move on.
0.372 + 0.366 + 0.362 +0.333 + 0.327 = 1.76
1.75 divide 5 = 0.352
"What is the median of the five batting averages?"I found the median to be 0.362."
"That is correct, can anyone tell me how Matthew found the answer of 0.362?"
"To find the median Matthew had to arrange the five batting averages in ascending order. Then because the number of averages is odd, the median is the middle value."
"I could not have said it better myself Amy, wonderful. Are there any questions on median?" No one raised his or her hand hand, so we move on.
0.327, 0.333, 0.362, 0.366, 0.372"What is the mode of the batting averages?"
"There is no mode."
"That is correct, Daniel why is there no mode?"
"The mode is the value that occurs the most often. Each batting average occurs just once, so there is no mode."
"Very good Daniel. Are their any questions regarding mode?" No one raises his or her hand, so we move on to range. "What is the range of the batting averages?"
"The range is 0.045."
"Wonderful Andrew. Can someone tell me how Andrew found the answer of 0.045?"
"Andrew subtracted the lowest value from the highest value in the set. This gave him an answer of 0.045."
0.372 – 0.327 = 0.045"Great job Emily. Now class, make sure that you all have the first example in your notes. Are there any questions over what we did?" Again, no one raised his or her hand. "Now we are going to move on to example 2."
Example 2:
Find the mean, median, mode, and range for each set of data.
3, 5, 8, 5, 8, 7, 16, 10, 2, 7, 1, 5, 6, 1
Solution:
"Can anyone tell me what the mean is?"
"The mean is 6. I divided the total which is 84 by the number of numbers in the data set which is 14."
"Great job Nate. Are there any questions on how to find the mean?" No one raises his or her hand. "Can some one tell me the median of the set."
"The median is 5.5. There is an even number of numbers and the middle falls between the seventh and eight numbers, which are 5 and 6. I added the two numbers and divided by 2 to find the median."
"Wonderful Daniel, and how did you know what to do when their is an even number of numbers?"
"The text told me that when there is an even number of values, you find the mean of the two middle values."
"Great job Daniel. Class if you did not have that in your notes, please add it now. Can someone tell me what the mode is?"
"The mode is 5 because 5 occurs most frequently. "
"Very nice Nik! Can someone tell me what the range for the data is?"
"The range is 15. I found this by subtracting 1 from 16."
"That is correct Erica. Now lets move on to part b."
Find the mean, median, mode, and range for each set of data.
160, 100, 150, 125, 125, 150, 114
"What is the mean for this set of data?""The mean is 132. I added the values together and divided it by 7, which is the number of values in the data set.
"Very nice Andrew. Can someone tell me what the median is?"
"The median is 125. There is an odd number of values, so the median was just the number in the middle."
"Great job, Randy. What is the mode of the data?"
"I got 125."
"I got 150."
"Both of you are correct. For this problem, there are two modes. A problem can have multiple modes if there are values that occur more frequently than others. Make sure you have included something in your notes on this. You never know what will be on the test on Friday. Can someone tell me what the range for the set is?"
"I found the range to be 60, by subtracting 100 from 160."
Example 3:
"Wonderful Amy. Are there any questions over example 2?" No one has any questions. "On to example 3. Can someone read example 3 to the class?...Yes Nate please read example 3.""Suppose that Dale has test scores of 75, 95, 82, and 77. He has one test remaining and his goal is to have a test average of exactly 85. What must Dale score on the final test in order to meet his goal?"
"Does anyone have any ideas on how to find out what Dale must score on his final test?"
"I think we should start by putting the values in order from highest to lowest."
"Great suggestion Nik, what would that look like then?"
"95, 82, 77, 75"
"Exactly. Now does anyone know what we can tell my placing the numbers in order?
"I noticed the highest and lowest scores are both 10 points from 85, so their average is 85 and they can be disregarded. The other two scores are both lower than 85, which means that the new score must be higher than 85 in order to balance these two scores."
"Wonderful observation Timmy. Does anyone know how we can calculate the exact score needed?"
"What if we add the values together and divide by 4?"
"That is close, but not exactly right. We need to account for the final test score. So we need to add the four values given, and an x, which will take the place of the final score. Then we need to divide this sum by 5 because we will be working with 5 values. We will set the whole equation equal to 85. When we do this we get 329 + x = 425. Then we solve for x. Can someone tell me what x equals?
"I got x = 96"
"Nice work Daniel. Can some on interpret this result? What does the 96 tell us?"
"It means that Dale must earn a 96 on his final test in order to have an average of 85 for his test grades."
"Wonderful Randy! Are there any questions on example 3?" No one has any questions. "Are there any questions on any of the material we have covered so far?" Again, there are no questions. "Let move on to example 4 then."
Example 4:"Ben, please turn around, and read for us example 4."
"Cathy has been swimming in the 50-meter butterfly event since she started high school. During that time, she has kept track of what place she finished in the event at each meet she attended. Find the mode, median, mean, and range of the places finished, using the data in the table below."
Place
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th Frequency
llll lll llll lllll
ll llll llll lll lll l "Thank you Ben. Everyone please look at the frequency table on page 189. Does someone know how I would find the mode of this data?"
"I think you just find the value in the frequency table that has the most tally marks. If that is the case then it would be fourth place. So the mode is 4th place."
"That is exactly right Nik. Great work! Are there any questions on mode and frequency tables?"
"What happens if two of the values in the frequency table have the most, like if there is a tie for the most?"
"Amy, that is a wonderful question. Then you would have two modes. Are there any other questions?" No one raises his or her hand. "Alright, does someone know how I would find the median of this data?"
"I think you first have to count the tally marks in the frequency table. Then you have to find the center tally mark. Next, you look to see in which column the center tally mark falls. That place will be the median. I found there to be 33 marks in the table. The location of the center tally mark is the 17th mark. I saw this was in the 5th place column. This means the median of the places finished is 5th."
"Wow, what a wonderful explanation Erica. Are there any questions on how to find median? No one raises his or her hand. "Make sure you understand how to find the median using a frequency table. It might come up on the test Friday. "Can someone tell me how to find the mean using a frequency table?""Well, I found the mean to be 5th place. I found this by first multiplying each place finished by the number of tally marks below it."
"Stop there for a second Andrew, how did you know to multiply there?"
"I multiplied because it would be the same as adding each value in the frequency table as many times as there are tallies."
"Excellent. You may continue explaining how you got 5th place as the mean."
"After I multiplied the numbers, I added the products and divided them by the total number of tally marks which is 33. When I did this, I got 5. I converted 5 into 5th place because of the type of data we are using."
"Very nice explanation. Thank you Andrew. Are there any questions on how to find the mean using a frequency table?" No one has a question. "Alright, can someone tell us how to find the range using a frequency table?"
"The range is just the difference between the highest and lowest places finished. So I subtracted one from ten to get 9. The range of the places finished is 9."
"Good job Nate. Now that you all have finished taking notes using the Cornell Note system, I want you to get with a partner. With your partner, I want you to formulate three questions based off your notes. Then I want you to practice reciting your notes. This can mean you ask each other the questions you formed and then require your partner to answer the question. To come up with questions, you may have to compare notes to insure you both have the same information. Use this time wisely as it will help you prepare for your upcoming test. Once all of your questions are written and you have practiced reciting your notes, I would like you to get started on a summary of the information learned. Do not worry if you do not finish your summary, it will not be due until tomorrow, so you can finish it tonight."
Allow students 20 minutes to work with their partners on questions, reciting, and a summary.
Check for Understanding
"Now it is time to see what you have learned. In your notes copy down the following chart from the overhead. Please do all of your own work. You may use your notes if they are needed."
Exercise to be done individually, then students will be asked to come to the board to show how they got their answers.
Exercise Mean Median Mode Range 1. 8, 10, 7, 15, 12 2. 84, 88, 92, 91, 85, 88 3. 124, 132, 105, 112, 161, 124, 124 4. 6.5, 4.8, 3.3, 4.8, 4.7, 6.5, 5.1 5. 53, 71, 90, 102, 88, 71, 52, 75 6. 52, 61, 66, 68, 41, 52, 60, 64 7. 0.8, 0.62, 0.35, 0.44, 0.58, 0.65 8. 16, 12, 8, 7, 3, 2, 15, 21, 2, 12 "Now I would like 8 volunteers to come forward and fill in the chart on the overhead. Thank you: Nik, Amy, Emily, Daniel, Randy, Nate, Erica, Andrew. Please correct your answers in your notes. You will want the correct answers to study from. Are there any questions over anything we have done today? No, okay then I have a few questions for you all."
Answers:
Exercise Mean Median Mode Range 1. 8, 10, 7, 15, 12 2. 84, 88, 92, 91, 85, 88 3. 124, 132, 105, 112, 161, 124, 124 4. 6.5, 4.8, 3.3, 4.8, 4.7, 6.5, 5.1 5. 53, 71, 90, 102, 88, 71, 52, 75 6. 52, 61, 66, 68, 41, 52, 60, 64 7. 0.8, 0.62, 0.35, 0.44, 0.58, 0.65 8. 16, 12, 8, 7, 3, 2, 15, 21, 2, 12 Sample of Cornell Notes
After Reading
VIII. Questioning
"Can some one explain the difference between mean and the median of a set of data?"
"According to the text we read, they are both forms of average. Yet, the mean is the average obtained from dividing the sum of all the terms by the number of terms. The median is the middle number in a set of data."
"Very good Timmy. Can some one explain how a frequency table makes it easier to find the mode?"
"The frequency table has tally marks. All you have to do is look at the chart, and see which number has the most tallies under it. It makes it faster."
"Thank you Andrew. How do you find the median from the frequency table?"
"You have to count the number of tally marks. Then find the middle number and look to see what number corresponds to that tally mark."
"Very good Erica, how did you know that answer?"
"It was in my notes under example 4."
"Wonderful. How is it possible to have more than one mode in a set of data?"
"If there is more than one number that is tied for the most frequent in a set of data, then you have two modes."
"Correct. Daniel how did you know that answer?"
"It was also in my notes under example 2."
"Wonderful. It seems like you all understand central measures of tendency. To insure we are all on the same page before starting our homework, we are going to take a short Quiz. Remember there is no talking during a quiz. Keep your eyes on your own paper. You will be given five minutes to answer the four questions."
IX. Writing to learn activity
"Please pass forward your quizzes. It is now time to take out your math journal. Date the page, and put the topic for today in the right hand corner. The questions are on the overhead. Please answer the questions to the best of your ability. The first question is asking you to discuss the strategy we worked with today. The second question looks at the measures of central tendency and how they might be used in certain situations. Today I will not be grading for grammar and punctuation. You have ten minutes to get started; whatever you do not finish, will be homework. Your math journals are due Friday."
1. How well did this strategy work for you all? Did you notice you were better organized? What is one benefit that you found of using the Cornell Notes? When could you use Cornell Notes again?
Sample answer: I thought the strategy worked really well for me. It helped me decide what to include in my notes and what could be excluded. I also liked writing questions and a summary based off our notes. I think it will really benefit me when it comes time to take a test. I believe Cornell Notes could be used again in both this class and my other classes. It is wonderful to have organized notes.
2. The concepts of mean, median, mode and range are used frequently. Give an example of how the measures of central tendency given below might be used in each situation:
a. Mean at school:_____________________________________________________________________
b. Mode in business:____________________________________________________________________
c. Range at home:______________________________________________________________________
d. Median in the newspaper:______________________________________________________________
e. Mean in sports:______________________________________________________________________
Sample answers:
a. Grades are given based on the mean of a student's scores.
b. The mode of a sales survey will show the product that people buy the most
c. The range of your monthly electric bills will help you estimate the amount you need to save for those bills.
d. Articles use the median to indicate a characteristic of the average person when the mean is not appropriate.
e. The mean shows the approximate number of points, hits, or saves a player usually makes in one game.
X. Closure
"Please wrap up the sentence you are writing right now, and look up at me. Our time today is almost up. We have looked at measures of central tendency. Scientists, marketing experts, political experts, and many other professionals use these. They are used when performing research projects. In these projects, they make a hypothesis and then prove it true or false. The data from these projects is then presented in books, newspapers, and magazines that students might read. As you all know, we are performing research projects. These will be published in a paper that is due on Friday. In your paper, you need to include the measures of central tendency on your data, and include a frequency table. This is the task that you will need to perform along with doing the homework. I want all of you to compute the central measures of tendency for your data from your survey. This includes a frequency table. Also, remember to finish your writing in your math journal, and writing the summary for your notes if you did not finish.
Your book assignment is on pages 190-191. I want you to work on problems 3-13, 15-57 odd, 59-69, and 70. These problems are to be done independently. Please do them to the best of your ability. We have five minutes left in class right now, so please get to work. If you have any questions, please raise your hand and I will be over. If tonight you have further questions, come and see me tomorrow morning. I will be in early. Tomorrow we will be looking at how to graph data, and which graphs are the best for our data. For this lesson, please bring in a recent newspaper or magazine. I have a few in the room, but it would be helpful if you could bring in others. We will be using them for our lesson."