Mean, Median, Mode and Range

Transcription

1 Mean, Median, Mode and Range 8 th grade 5 days of 40 minute class periods Materials used: internet, TI-83, tape measures, magazines and newspapers Kimberly Best 1

2 Table of Contents Objectives: page 3 Standards: page 3 Materials: page 3 Overview of Unit: page 4 Lesson Plans (including worksheets): Day 1: page 5 Day 2: page 7 Day 3: page 9 Day 4: page 11 Day 5: page 15 Assessment: page 16 2

3 Objectives: By the end of this unit students will be able to find the mean, median, mode, and range of various sets of data. Students will also be able to collect and analyze data using a variety of methods. Standards: NCTM Standards: Number and Operations, Data Analysis Students will be adding, subtracting, and dividing daily. Students will also be analyzing data in various forms. New York State Key Ideas: 5D Use of statistical methods and measures of central tendencies to display, describe, and compare data. Students will be finding mean, median, mode and range daily. They will be getting data from charts, tables and surveys. The students will also make graphs from the data they collected. Materials: Calculator Internet Tape Measures Student Worksheets Graphs from newspapers, or magazines Scott Foresman, Transition Mathematics, 1998 Glencoe, Mathematics Course 3, Practice 3

4 Overview of Unit In this unit students will be introduced to mean, median, mode and range. They will have to find the measures of central tendencies from a variety of data. They will also have to gain data themselves. Day 1: Introduction to measures of central tendency. Day 2: Students look at the internet to find current data. Students analysis the data, then find measures of central tendencies from select data. Day 3: Students will measure their heights then find the measures of central tendencies. Day 4: Students will find measures of central tendencies from charts and graphs. Day 5: Students will practice finding mean, median, mode and range. Assessment: Students will interview people make a frequency table, graph and find the measures of central tendencies. All homework is out of Scott Foresman, Transition Mathematics, 1998, unless otherwise noted. 4

5 Day 1 Objective: Students will define and find the mean, median, mode and range of given data. Standards: NCTM Standards: Number and Operations, Data Analysis New York State Key Ideas: 5D Materials: student notebooks calculators Opening: The following question is placed on the front board for students to answer as they come into class. If you received the following grades on your tests, what should your grade be on your report card and why? 75, 95, 80, and 90 Main: Notes: on the overhead, vocabulary and problems, students coping and solve. Do first three or four examples together, then let students work on the rest of the examples by themselves or with a partner. Closing: Have students go to the board and put their solutions on the board. Hand out and discuss the Unit Project Homework: Unit Project Assessment: As students are working walk around and make sure they are on task. Student work on the board at the end of class. Teacher s Notes: Make sure students are rounding, adding and dividing negatives correctly for the mean. For the median check to see if students are putting numbers in order before find the middle number. 5

6 Day 1 transparency Mean- The average of a set of numbers. To find add all numbers together and divide by the number of numbers you have. Median- The middle number of a set of numbers when numbers are placed in order. To find the median place numbers in order from least to greatest and then find the number in the middle. If there is an even number of numbers find the average of the two numbers in the middle. Mode- The number that occurs the most. To find the mode find the number that occurs more than the others, there can be two modes, if there are no modes write none. Range- The difference between the largest and smallest number. To find the range subtract the largest and the smallest number. For the following examples find the mean, median, mode and range. Round the mean to the nearest tenth. 1. 2, 6, 1, 5, , 4, 5, 5, 8, , 4, -3, 3, 4, , -8, -5, 6, 7, -8, , 8, 4, -8, -4, 8, 4, -8, , 5, , 0, -2, , -3, -4, 5 6

7 Day 2 Objective: Students will gather data from the internet and find mean, median, mode and range from the data. Standards: NCTM Standards: Number and Operations, Data Analysis New York State Key Ideas: 5D Materials: Computer lab, with internet access Student Worksheet Calculator Opening: In what state do you think the highest temperature occurred yesterday, and in what state do you think the lowest temperature occur last night? Main: Have students go to the following website from the National Weather Service Students will find the high and low temperatures for the past 2 days. Explain what the information given to them represents. Answer the opening question and give a prize to the student who was the closest. Students will use this data to answer the questions on the student worksheet. Assign half of the class to work with one day and the other half to answer the question based on the other day. Closing: Have students close out of the internet and discuss their findings, based on question 10. Homework: page Unit Project Assessment: As students are working walk around and make sure they are on task. Teacher s Notes: Make sure they are using the same date and looking at all of the data. Some students may have to print off the data so they can highlight the numbers they are looking for. 7

8 Name Weather Worksheet Date Class Answer the following questions. If work needs to be shown, show it below the problem. 1. What is the date of your data? 2. What is the high temperature for Columbus, Georgia?, Columbus, Ohio? 3. What is the low temperature for Peoria, Illinois?. 4. What is the range in high temperatures between Harrisburg, Pennsylvania, Las Vegas, Nevada and Fairbanks, Alaska? (show work) 5. What is the mean low temperatures of all cities that begin with P? (show work) 6. What is the mode high temperature for all cities? 7. What is the median amount of precipitation for all cities? (show work) 8. What is the range of high and low temperature of Nashville Tennessee? (show work) 9. What city has the greatest range between high and low temperatures? (show work) 10.Based on the forecast for tomorrow what city would you like to visit? 8

9 Day 3 Objective: Students will find their heights then find how they compare to the class. Students will make analyze a box and whiskers plot and find mean median mode and range of the class data. Standards: NCTM Standards: Number and Operations, Data Analysis, Measurement New York State Key Ideas: 5A, 5D Materials: Tape measure Calculator Student Worksheet Opening: Students will be asked to write down some generalizations about what they believe to be true about the class height. Main: Students will work in pairs and measure their heights in centimeters. Students will then record the heights on the chart taped to the front board. Also students will input their data into a list on the TI- 73 calculator. Chart is separated into males and females. Once everyone is finished the class will have a discussion about the tallest, shortest height. Are there any heights that do not make sense? Students will work in pairs to find the mean, median mode and range of the entire class data, male data and female data. Closing: We will then see if there are any patterns, or is the data what they expected to discover. From the lists on the calculator, make a box and whiskers plot of the males and the females. See the data from the box and whiskers plot match what the students found to be true. Homework: Unit Project Assessment: As students are working walk around and make sure they are on task. Teacher s Notes: Make sure students understand that the tape measure is not as tall as the students and they need to add an amount to it. Having two calculators one for the females and one for the males to input data, may be useful not to confuse the data. Then transfer the lists to one calculator. 9

10 Name Date Student Measurement Class What is your height measured in centimeters? (Remember the tape measure is not as tall as you) Record the class s heights below 1. What is the tallest male height? 2. What is the shortest female height? 3. What is the median of all heights? 4. What is the mode of all heights? 5. What is the mean of the male heights? 6. What is the mean of the female heights? 7. What is the range of the class heights? Day 4 Objective: Students will find the mean, median, mode, and range from graphs, tables and charts. Standards: NCTM Standards: Number and Operations, Data Analysis New York State Key Ideas: 5D Materials: Student Worksheet Calculator Opening: Look at the chart on the overhead and discuss what can be determine from the graph. Main: Work on the first problem together. Students will work by themselves to finish the student worksheet. Closing: Review the worksheet 10

11 Homework: Unit Project Go through the newspaper or a magazine, find a chart or table cut it out, staple to the homework assignment. Students need to find the mean, median, mode and range. Assessment: Student worksheet and homework. Teacher s Notes: Students need to be aware the mode is the tallest bar on the graph, not the height of the bar that happens most. Have a supply of newspaper or magazines for students that do not have any available at home. 11

12 transparency Time to get to school People :00-1:30 1:31-2:00 2:01-2:30 2:31-3:00 3:01-3:30 Minutes What can be determined by looking at this graph? Is it appropriate to use a bar graph to show this data? 12

13 Name Graphs and Data Date Class Look at the following graph and answer the following questions. 1. Favorite Colors red blue green purple black white 1. What color is the mode? 2. How many people were surveyed? 2. Test scores frequency How many students were tested? 2. What is the mean test score? 3. What is the median test score? 4. What test score is the mode? 3. 13

14 Shoe Sizes Shoe sizes 1. What is the range of shoe sizes? 2. What is the mode of show sizes? 3. What is the mean shoe size? 4. What is the median shoe size? 4. Rain fall for October Rain fall (inches) Days more than What is the range of rain fall? 2. What amount of rain fall is the mode? 3. What is the mean amount of rain fall? 4. What is the median amount of rain fall? 14

15 Day 5 Objective: Students will practice finding mean, median, mode and range Standards: NCTM Standards: Number and Operations, Data Analysis New York State Key Ideas: 5D Materials: Student Worksheet Calculator Opening: Write down the definition and how to find the mean, median, mode and range. Main: Students will get in groups of four and compare the graphs they found for homework and tell the other group members how they found the mean, median, mode and range. Students will work on Glencoe, Mathematics Course 3, Practice 4-4 worksheet. Add to directions find the range. Closing: Review the answers Homework:Unit Project Assessment: As students are working walk around and make sure they are on task. Teacher s Notes: Make sure students are showing work 15

16 Name Unit Project Date Class During this week you must survey between 40 and 50 people. You may ask them any question that will result in your ability to find the mean, median, mode and range of the data. Some examples: shoe size time to get to school/work time they wake up time they go to bed time to get ready in the morning age year they were born amount of time they watch TV per day/ week Your data must be organized and answers labeled, showing the mean, median, mode and range. Your data should be presented in a frequency table and a graph Due next Monday 16