4.5 Scatter Plots and Trend Lines

Size: px

Start display at page:

Download "4.5 Scatter Plots and Trend Lines"

Raymond Dixon
6 years ago
Views:

Name: 1 Scatter Plot: 4.5 Scatter Plots and Trend Lines EXAMPLE 1: a. The data in the table shows a survey of 12 adults for their height (cm) and their wingspan (cm).

1 Name: 1 Scatter Plot: 4.5 Scatter Plots and Trend Lines EXAMPLE 1: a. The data in the table shows a survey of 12 adults for their height (cm) and their wingspan (cm). Create a scatter plot of the data. Is there any relationship between to the two sets of data? Wingspan (cm) Height (cm) If two sets of data show a relationship, it is called a There are three types of relationships that the two sets of data may have:

2 2 b. The table shows the number of species added to the list of endangered and threatened species in the United States during the given years. Create a scatter plot of the data. Is there a relationship between the two sets of data? Calendar Year Species EXAMPLE 2: Identifying Correlations Would you expect the following sets of data to have a positive, negative, or no correlation? a. The amount of time you have and the number of classes you take. b. The sales of shovels and the amount of snowfall. c. The length of a baby at birth and the month it was born. d. A high-school sprinter's age and the time it takes to finish a 100 meter race. CREATE: With your partner, describe three situations: one that shows a positive correlation, one that shows a negative correlation, and one that shows no correlation.

3 3 Scatter Plots Homework 1. The table shows the number of soft drinks sold at a small restaurant from 11:00 am to 1:00 pm. Graph a scatter plot using the given data. 2. The table shows the percent of people ages who reported they voted in the presidential elections. Graph a scatter plot using the given data. 3. Would you expect to see a positive, negative, or no correlation between the data sets? Explain. a. The temperature during the day and the number of people in the pool. b. The height of an algebra student and the number of phone calls they make in one week. c. the number of pets a person has and the number of times they go to the pet store. d. the number of chicken pox vaccines given and the number of chicken pox cases reported.

4 4 4.5 Trend Lines and Linear Regression Trend Line: EXAMPLE 1: Writing a Trend Line a. The table shows data students collected on their test scores and the number of hours they watched television the previous day. Make a scatter plot of the data. Does the data appear to have a relationship? Hours Watched Test Score Draw a trend line through the data. Write an equation for the trend line.

5 5 b. The table lists the number of events in the Winter Olympic Games from 1972 to Create a scatter plot of the data. Does there appear to be a relationship between the sets of data? Year of the games Number of events Draw a trend line through the data. Write an equation for the trend line.

6 EXAMPLE 2: Linear Regression on the Graphing Calculator a. The table gives the distance (in meters) that a discus was thrown by men to win the gold medal at the Olympic Games from 1980 to Use a graphing calculator to find the line of best fit. Year Men's Gold Medal Discus Throw (m) b. The table shows the annual cost of attending Michigan State University as an in-state student from 2000 to Use a graphing calculator to find the line of best fit. Use your function to approximate the cost for your freshmen year of college. Year Cost of Tuition

7 How to Perform a Linear Regression on the Graphing Calculator Enter your data into the list feature on the

(you don't have to change the name of the list if you don't want to) Start a new document and choose Add Lists

Enter the table into the calculator by typing in the number and pressing enter.

To generate a scatter plot, press the DOC button, scroll down to option 4: Insert, and then choose 7 Data &

7 7 How to Perform a Linear Regression on the Graphing Calculator Enter your data into the list feature on the calculator. (you don't have to change the name of the list if you don't want to) Start a new document and choose Add Lists & Spreadsheet or go to the HOME screen and choose the spreadsheet option at the bottom of the screen. Enter the table into the calculator by typing in the number and pressing enter. You can change the name of the list to keep your data organized. To generate a scatter plot, press the DOC button, scroll down to option 4: Insert, and then choose 7 Data & Statistics. This will create a scatter plot for you. You can add your variables to the x and y axis should you choose. To add the axis labels, use the cursor, scroll over the x-axis and choose the variable you entered into list A, then scroll over the y-axis and choose the variable you entered into list B.

8 Performing a Linear Regression Now that the data is in the calculator, we can use it to generate

From the scatterplot screen, press the DOC button, and go down to option 3: Calculator and press

Now, press MENU, go to 6: STATISTICS, then down to 7: STATS TESTS, and in the STATS TESTS menu

The part that we care about is the line that says RegEqn - a + bx because this screen gives us the

variables that you entered into the calculator for your lists.

pages on the calculator. Leave this number as whatever is there when the screen opens.

8 8 Performing a Linear Regression Now that the data is in the calculator, we can use it to generate the trend line for us. From the scatterplot screen, press the DOC button, and go down to option 3: Calculator and press enter. This will add a new calculator screen. Now, press MENU, go to 6: STATISTICS, then down to 7: STATS TESTS, and in the STATS TESTS menu scroll down to A: LINEAR REGRESSION TEST. All of this information should have showed up. The part that we care about is the line that says RegEqn - a + bx because this screen gives us the values of a and b to be able to write an equation of a trend line Change the x and y lists to the variables that you entered into the calculator for your lists. The Save RegEqn to will put the equation for the trend line of the data into one of the function pages on the calculator. Leave this number as whatever is there when the screen opens. Then press enter. To add the trend line to your scatterplot, use the touchpad to navigate back to the scatterplot screen. Press MENU and select 4: ANALYZE followed by 6: REGRESSION. From there, choose option 2: LINEAR (a + bx). The line will appear on your scatter plot and equation will be shown.

9 bar graph 10.1 Organizing and Displaying Data Reading and Interpreting Graphs EXAMPLE 1: Reading and Interpreting Bar Graphs Use the graph to answer the questions a.

Which ingredient contains the least amount of fat? e. Which ingredients contains at least 8 grams of fat? double bar graph: EXAMPLE 2: Reading and Interpreting Double Bar Graphs a.

9 9 bar graph 10.1 Organizing and Displaying Data Reading and Interpreting Graphs EXAMPLE 1: Reading and Interpreting Bar Graphs Use the graph to answer the questions a. Which ingredient contains the most fat? b. How many more grams of fat are in ham than in turkey? c. How many total fat grams are in the sandwich? d. Which ingredient contains the least amount of fat? e. Which ingredients contains at least 8 grams of fat? double bar graph: EXAMPLE 2: Reading and Interpreting Double Bar Graphs a. In which year did State College have the greatest average attendance for basketball? b. On average, how many more people attended a football game than a basketball game in 2001? c. Which years had the same average basketball attendance? What was the average attendance for those years?

During which 4 hour time period did the temperature increase the most? c.

10 10 Line graph: EXAMPLE 3: Reading and Interpreting Line Graphs a. At what time was the temperature the warmest? b. During which 4 hour time period did the temperature increase the most? c. What is the difference in temperature from 4 AM to noon? Double line graph: EXAMPLE 4: Reading and Interpreting Double Line Graphs a. In which months did airline B charge more than airline A? b. During which months was the cost the same?

11 11 Circle Graph (pie chart): EXAMPLE 5: Reading and Interpreting Circle Graphs a. Which two fruits together make up half of the fruit salad? b. Which fruit is used more than any other?

12 Check Your Skills 1. Use the double bar graph to answer the following questions a. Which was the first year that the Barnes rented more DVDs than VHS tapes? b. About how many videos did the Barnes rent in all in 2003?

12 12 Check Your Skills 1. Use the double bar graph to answer the following questions a. Which was the first year that the Barnes rented more DVDs than VHS tapes? b. About how many videos did the Barnes rent in all in 2003? 2. Use the line graph to answer the following questions a. During which time interval did the car's speed increase the least? b. Describe how the speed changed over time. 3. Use the circle graph to answer the following questions. a. There were 5 times the number of orders for as there were strawberries. b. What percent of the orders for ice cream were mint chip or vanilla?

13 13 frequency table: 10.2 Organizing Data Creating Frequency and Relative Frequency Tables EXAMPLE 1: Creating Frequency Tables a. The final scores for each golfer in a tournament are given below. Use the data to make a frequency table with intervals. 77, 71, 70, 82, 75, 76, 72, 70, 77, 74, 71, 75, 68, 72, 75, 74 b. The number of students enrolled in Western Civilization classes at a university are given. Use the data to make a frequency table with intervals. 12, 22, 18, 9, 25, 31, 28, 19, 22, 27, 32, 14

14 14 EXAMPLE 2: Calculating Relative Frequencies a. RAW DATA Favorite Football Team Michigan State University I don't care about Football University of Michigan Other Total Frequency Frequency as Percents (relative frequency) Favorite Football Team Michigan State University I don't care about Football University of Michigan Other Total Relative Frequency How can you check that you have correctly converted frequencies to relative frequencies? Explain why the number in the total column of a relative frequency table is always 1 (or 100%). EXAMPLE 2: Creating a Two Way Frequency Table Favorite Movie Genre Comedy I don't care Action Drama Horror Other Total Boy Girl Total Calculate the Relative Frequencies Favorite Movie Genre Comedy I don't care Action Drama Horror Other Total Boy Girl Total

15 Frequency Tables and Relative Frequency Homework 1. The number of calls per day to a fire and rescue service for three weeks is given. Use the data to complete the frequency table. 2.

15 15 Frequency Tables and Relative Frequency Homework 1. The number of calls per day to a fire and rescue service for three weeks is given. Use the data to complete the frequency table. 2. The number of calls per day received by a traveling Vet Van service for three weeks is given. Use the data to make a frequency table with intervals. 3. Antonio surveyed 60 of his classmates about their participation in school activities as well as whether they have a part-time job. The results are shown in the two-way frequency table below. Use the table to complete the exercises. Job Job Complete the table by finding the row totals, column totals, and the grand total. Activity Clubs Only Sports Only Both Neither Total Yes No Total Create a two-way relative frequency table using decimals. Activity Clubs only Sports Only Both Neither Total Yes No Total

16 16 Check Your Skills The owners of an ice cream shop conducted a survey regarding customers' favorite flavors. The owner asked 80 randomly selected customers whether they preferred vanilla, chocolate, or strawberry. The results are shown in the frequency table below. Flavor Vanilla Chocolate Strawberry Total Frequency Convert this table into a relative frequency table using decimals Flavor Vanilla Chocolate Strawberry Total Relative Frequency 2. The owner also recorded the gender of each customer. The results are shown in the two-way frequency table. Complete the table. Gender/Flavor Vanilla Chocolate Strawberry Total Male Female Total 3. Create a two-way relative frequency table for the data in the table. Gender/Flavor Vanilla Chocolate Strawberry Total Male Female Total

EXAMPLE 1: From Frequency Table to Histogram a. First, let's collect some data.

17 17 Frequency and Histograms BAR GRAPHS vs. HISTOGRAMS What are the similarities between the two? What are the differences? EXAMPLE 1: From Frequency Table to Histogram a. First, let's collect some data...what day were you born? Then organize the data into a frequency table. Then create a histogram. Describe the shape of the data: is it symmetric or skewed left or right?

18 18 b. Make a histogram for the number of days for Maria's last 15 vacations. 4, 8, 6, 7, 5, 4, 10, 6, 7, 14, 12, 8, 10, 15, 12 c. Make a histogram for the heights of basketball players (in inches) on the team 72, 68, 71, 70, 73, 69, 79, 76, 72, 75, 72, 74, 68, 70, 69, 75, 72, 71, 73, 76

19 10.2 Frequency and Histograms Homework 1.

Use the data to make a frequency table and histogram of the data. 2.

19 Frequency and Histograms Homework 1. The finishing times of runners in a 5K race, to the nearest minute are given. Use the data to make a frequency table and histogram of the data. 2. The breathing intervals of gray whales are given. Use the frequency table to create a histogram for the data. 3. The weights of 50 kittens are given. Use the data to create a frequency table and histogram of the data.

20 20 Check Your Skills 1. The heights in inches of the 2015 NBA All-Star Game players from the Eastern Conference are given. Use the data to complete a frequency table and histogram The heights in inches of the 2015 NBA All-Star Game players from the Western Conference are given. Use the data to complete a frequency table and histogram

21 21 Data Distributions Measures of Central Tendency and Stem-and-Leaf Plots stem-and-leaf plot: EXAMPLE 1: Creating a Stem-and-Leaf Plot a. The number of students in each of the elective classes at school are given. Use the data to make a stem-and-leaf plot. 24, 14, 12, 25, 32, 18, 23, 24, 9, 18, 34, 28, 24, 27 b. The temperature in degrees Celsius for two weeks are given below. Use the data to make a stem-andleaf plot. 7, 32, 34, 31, 26, 27, 23, 19, 22, 29, 30, 36, 35, 31 mean: median: mode: range:

22 22 EXAMPLE 2: Finding Mean, Median, Mode, and Range Find the mean, median, mode, and range for each set of data a. Stem Leaf b. The number of hours Isaac did homework on six days: 3, 8, 4, 6, 5, 4 c. Stem Leaf d. The data shows the number of years that each monarch of Great Britain reigned from King George III to Queen Elizabeth II. Find the mean, median, mode, and range of the data. Monarch George III 59 George IV 10 William IV 7 Victoria 63 Edward VII 9 George V 25 Edward VIII 1 George VI 15 Reign (years) Why are mean, median, and mode called the measures of central tendency?

23 EXAMPLE 3: Choosing a Measure of Central Tendency a. Niles scored 70, 74, 72, 71, 73, and 96 on six geography tests. Use the mean, median, and mode of his scores to answer the following questions. Which value gives Niles' test average? 23 Which value best describes Niles' scores? Explain. b. Josh scored 75, 75, 81, 84, and 85 on five tests. Use the mean, median, and mode of his scores to answer the following questions Which values describes the score that Josh received most often? Which value best describes Josh's scores? Explain. EXAMPLE 4: Writing an Equation a. Suppose your grades on three history exams are 80, 93, and 91. What grade do you need on your next exam to have a 90 average on the four exams? b. Suppose your grades on three science exams are 82, 94, and 89. What grade do you need on your next exam to have an average of 90?

24 24 Data Distributions Homework 1. The number of rushing yards completed by Jeremy Langford at Michigan State in each of his 2014 games is listed. Use the data to make a stem-and-leaf plot Find the mean, median, mode, and range for the data. Mean: Median: Mode: 2. The number of points scored by Travis Trice in Big Ten games during the basketball season are given. Use the data to create a stem-and-leaf plot Find the mean, median, mode, and range for the data. Mean: Median: Mode: Which measure of central tendency best describes Travis Trice's points scored during the Big Ten season?

25 25 3. The amount's of Cathy's last six clothing purchases were $109, $72, $99, $15, $99, and $89. Find the mean, median, and mode of the data, and use them to answer the following. Mean: Median: Mode: a. Which value describes the average of Cathy's purchases? b. Which value would Cathy tell her parents to convince them that she is not spending too much on clothes? c. Which value would Cathy tell her parents to convince them that she needs an increase in her allowance?

26 26 Check Your Skills 1. The data shown is the total ice time, to the nearest minute, of Jonathon Toews in the 2015 Stanley Cup playoffs so far. Create a stem-and-leaf plot of the data. Find the mean, median, mode, and range of the data The data shown is the number of saves made by Carey Price of the Montreal Canadiens in the 2015 Stanley Cup Playoffs. Create a stem-and-leaf plot of the data. Find the mean, median, mode, and range of the data

27 Data Distributions Box and Whisker Plots RECALL: What is the median of a set of data? Quartiles: First Quartile (Q1): Third Quartile (Q3): Interquartile Range (IQR): Box-and-Whisker Plot: EXAMPLE 1: Creating a Box-and-Whisker Plot a. The data in the table shows the number of gold medals won by the top 15 medal winning teams in the 2012 Summer Olympics in London. Team Gold Medals Find the median, Q1, and Q3 of the data. United States 46 China 38 Great Britain 29 Russia 24 South Korea 13 Germany 11 France 11 Italy 8 Hungary 8 Australia 7 Japan 7 Kazakhstan 7 Netherlands 6 Ukraine 6 New Zealand 6 What is the IQR? Create a box-and-whisker plot for the data

28 28 b. Find Q1, Q3, and the IQR of the data. Create a box-and-whisker plot for the data. Let's gather our own data: How many texts do you send in a day? EXAMPLE 2: Comparing Data Using Box Plots a. The tables below list the average ages of players on 15 teams randomly selected from the 2010 teams in the NFL and the MLB. Compare the average ages of NFL players to the average ages of MLB players. NFL Average Ages Bears 25.8 Bengals 26 Broncos 26.3 Chiefs 25.7 Colts 25.1 Eagles 25.2 Jets 26.1 Lions 26.4 Packers 25.9 Patriots 26.6 Saints 26.3 Seahawks 26.2 Steelers 26.8 Texans 25.6 Titans 25.7 MLB Average Ages Astros 28.5 Cardinals 29 Cubs 28 Diamondbacks 27.8 Dodgers 29.5 Giants 29.1 Marlins 26.9 Mets 28.9 Nationals 28.6 Padres 28.7 Pirates 26.9 Phillies 30.5 Reds 28.7 Rockies 28.9 Yankees 29.3

29 29 NFL MLB Mean: Mean: Median: Median Q1: Q3: IQR: Q1: Q3: IQR: Create box-and-whisker plots of the data on the same number line to compare the spread: Based on a comparison of the measures of center (what are those again?), what conclusion can you draw about the typical age of an NFL player vs. an MLB player? Based on the measures of spread (what about these?), what can you conclude about the ages in each league?

30 30 Data Distributions Box-and-Whisker Plot Homework 1. The following data shows Steph Curry's points scored in each game during the month of March of the season. Complete the following table and make a box-and-whisker plot to represent the data Minimum First Quartile Median Third Quartile Maximum 2. The following data shows Max Scherzer's strike-outs in each of his starts during the 2014 season not including the playoffs. Complete the following table and make a box-and-whisker plot to represent the data Minimum First Quartile Median Third Quartile Maximum

31 31 3. The following data shows the point totals of Patrick Kane of the Chicago Blackhawks and Zach Parise of the Minnesota Wild during the month of January this year. Complete the following table and answer the questions that follow. Kane Parise Patrick Kane Center Spread Mean Median IQR Range Zach Parise a. Create box-and-whisker plots on the same number line to compare the data. b. Based on the comparison of the measures of center, what conclusion can you make about Kane's points vs. Parise's points. c. Based on the measures of spread, what can you conclude about Kane's points vs. Parise's points.

32 32 Check Your Skills 1. The frequency table shows the results of a survey of 60 teenagers on their favorite pizza toppings. Convert the frequency table into a relative frequency table using decimals. Favorite Pizza Topping Cheese Pepperoni Sausage Other Total Frequency Favorite Pizza Topping Relative Frequency Cheese Pepperoni Sausage Other Total 2. Below are the listed heights of the players on the Detroit Redwings and the Chicago Blackhawks in inches. Create a box-and-whisker plot of each set of data on the same number line. Chicago Blackhawks Detroit Redwings Calculate the mean of each set of data Based on the comparison of the measures of center, what conclusion can you make about the average height of a Blackhawks player vs. a Redwings player? Based on the measures of spread, what can you conclude about the heights of the players on each team?

33 Misleading Graphs and Statistics EXAMPLE 1: a. The salaries of 12 teachers are listed (in thousands) 25, 30, 35, 35, 35, 40, 40, 40, 45, 45, 50, 60 Create a line plot of the data Complete the following table based off the data Mean Median Range IQR Is the line plot displaying quantitative data or qualitative data? (what do those words mean?) Describe the overall shape of the data Which data value appears to be different than the others? Explain. Is it an outlier?

34 34 Now let's take the same data and add the salary of the superintendent 25, 30, 35, 35, 35, 40, 40, 40, 45, 45, 50, 60, 185 Create a line plot of this data Complete the same table for this set of data Mean Median Range IQR Complete each statement about the change for each measure (increased by... decreased by...) The mean The median The range The IQR Which data value appears to be different than the others? Explain. Is it an outlier? Which measure of central tendency is most affected by the outlier? Which measures of spread are affected?

35 35 SHAPES OF DISTRIBUTION EXAMPLE 2: Comparing Data Distributions The tables list Sierra's and Jacey's scores on math tests in each quarter of the school year. Create a line plot for each student's scores and identify the distribution as symmetric, skewed to the left, or skewed to the right. Sierra's Scores I II III IV Jacey's Scores I II III IV

36 36 Misleading Statistics Homework 1. Rounded to the nearest $50,000, the values (in thousands of dollars) of homes sold by a realtor are listed. Use the number line to create a line plot for the data set Complete the following table based on the data Mean Median Range IQR Suppose the realtor sells a home for $650,000. Which statistics are affected when 650 is included in the data set? Calculate the mean and median for the data now including the 650. Why might the realtor want to use the mean instead of the median when advertising the typical value of homes?

37 37 2. The table shows Chloe's scores on math tests in each quarter of the school year. a. Use the number line below to create a line plot Chloe's Scores for Chloe's scores. I II III IV b. Complete the table for the data set Mean Median Range IQR c. Do there appear to be any outliers in the data? Which of the statistics would change if the outliers were removed? d. Describe the shape of the distribution (skewed left, skewed right, or symmetrical). e. Which measure of center (mean, median, mode) should be used to describe the data?

0-13 Representing Data

0-13 Representing Data 1. SURVEYS Alana surveyed several students to find the number of hours of sleep they typically get each night. The results are shown in the table. Make a bar graph of the data. Draw a histogram to represent