Plotting Coordinates

Transcription

1 Plotting Coordinates Goal: identify coordinates of points and plot points on a cartesian plane A cartesian plane is a grid with a horizontal and a vertical The axes divide the plane into four. The point where the axes intersect is called the. An ordered pair identifies any coordinate on the graph and is written in the form. The x value of the coordinate is always written. The y value of the coordinate is always written. PRACTICE 1. Plot and label the following coordinates on the cartesian plane. A(2, 5) B(-5, 5) C(0, 4) D(-2, 0) E(4, -3) F(-4, -2) 2. Identify the coordinates of each point shown on the graph. A (, ) B (, ) C (, ) D (, ) E (, ) F (, ) Page 1 of 13

2 Interpreting Trends & Relationships in Scatter Plots Goal: investigate relationships between two variables A scatter plot is a graph that shows the relationship between variables. The points in a scatter plot often show a pattern, or. From the pattern or trend you can describe the. Carefully consider each of the three scatter plots below and answer the questions which follow. 1. The graph shows the plotted points rising upwards to the right. 2. As the length of the tibia increases the length of the leg increases. 3. The graph can be used to determine the length of a person's leg if you know the length of the tibia bone. 1. The graph shows the plotted points falling to the right. 2. As the distance from the net increases the number of baskets made decreases. 3. The graph can be used to determine the number of baskets you will make if you know the distance from the basket. 1. The graph shows the plotted points scattered. 2. As the age of the house increases the price of the house is either large or small. 3. The graph can't be used to determine the price of the house if you know how old it is. Page 2 of 13

3 VARIABLES: The dependent variable is located on the axis. This variable is changed by the other variable. The independent variable is located on the axis. This variable is NOT changed by the other variable. Identify the independent and dependent variables in each situation. a) Does the outdoor temperature affect the amount of fuel needed to heat a house? b) Is there a relationship between people s age and their heights? c) Does the amount of rain in a region depend on its latitude? TREND: Rises or falls to the right Rises to the right Falls to the right No trend CORRELATION: How close together points are in the trend Strong Correlation Moderate Correlation Weak Correlation No Correlation RELATIONSHIP: As the x-axis increases (bottom) the y-axis either increases or decreaes POSITIVE both increase As, NEGATIVE one increases, one decreases As, No relationship Page 3 of 13

4 Labelling a Graph!! (Very important things to label) Example Julie gathered information about her age and height from the markings on the wall in her house. Age (years) Height (cm) a) Identify the variables. Note: The independent variable comes first in the table of values. Independent: Dependent: b) Label the graph. c) Describe the trend in the data. d) Describe the correlation in the data. e) Describe the relationship. Page 4 of 13

5 Interpreting Trends & Relationships Worksheet 1) A basketball coach recorded the amount of time each player played and how many points the player scored in one game. a) Label the graph b) Plot the data Time (min) c) Describe the trend in the data Point Scored d) Describe the correlation e) Describe the relationship 2) The table below shows the sales of bottled water at a refreshment booth at the Canadian National Exhibition in Toronto, for different days during a heat wave one summer. Temperature Bottles Sold a) Draw a scatter plot and label the graph b) Describe the trend in the data c) Describe the correlation d) Describe the relationship Page 5 of 13

6 Line of Best Fit Goal: Infer information from a scatter plot using a line of best fit To be able to analyze and make predictions about data in a scatter plot, we need to the data using a or of best fit Rules for drawing a line of best fit: 1. The line must follow the. 2. The line should go through points as possible. 3. There should be the number of points and the line. 4. The line should pass through points the line, not just at the. Making Predictions Interpolating & Extrapolating 1. Use a ruler to draw a line of best fit (LOBF) through the data points 2. Start on the axis that you are given information about draw dotted line up/over to the LOBF 3. Now turn and draw a dotted line to the opposite axis this is your answer/prediction Interpolate You are making an estimation the range of known data. These estimations are usually the LOBF. Extrapolate Making a prediction the range of known data. Often requires you to the LOBF. These predictions are reliable. Example Use your line of best fit (LOBF) to estimate the following: Question Answer Method of Prediction a) How tall was Julie when she was 5 years old? b) How tall will Julie be when she is 9 years old? c) How old was Julie at 100 cm tall? d) How tall was Julie when she was born? Page 6 of 13

7 More About Correlation Direction A scatter plot shows a correlation when the pattern rises up to the right. This means that the two quantities increase together. A scatter plot shows a correlation when the pattern falls down to the right. This means that as one quantity increases the other decreases. A scatter plot shows correlation when the points are very spread out and no pattern appears. Hint: If the points are roughly enclosed by a circle, then there is no correlation. Strength of Correlation Strong: The points nearly form a Moderate: The points are somewhat, but still form a wide line Weak: The points are dispersed more widely, but still have a noticeable To help you visualize this, enclose the plotted points in an oval. If the oval is very narrow, the correlation strength is strong. If the oval is thin, the correlation is moderate. If the oval is fat, the correlation is weak. Example For each graph below: a) Draw a line of best fit b) Describe the trend and correlation c) Label the axes with possible variables that the graph might model and describe the relationship i. ii. iii. iv. Trend: Correlation: Trend: Correlation: Trend: Correlation: Trend: Correlation: Relationship: Relationship: Relationship: Relationship: Page 7 of 13

8 Line of Best Fit Worksheet 1) What is the relationship between the amount of rainfall and the duration of time it rains? a) Draw a scatter plot and a line of best fit for the data set below. Label the axes and include a title. Time (hr) Rainfall (ml) b) Describe the trend c) Describe the correlation d) Describe the relationship e) Use your line of best fit (LOBF) to determine how much rainfall at 6.5 hours. Show the dotted lines on the graph used to find your prediction. f) Is your answer to e) interpolation or extrapolation? Explain how you know. g) Use your LOBF to determine the number of hours to have 14 ml of rain. Show the dotted lines on the graph used to find your prediction. h) Is your answer to g) interpolation or extrapolation? Explain how you know. Page 8 of 13

9 2) What is the relationship between the price of a book in Canada compared to the price in the US? a) Draw a scatter plot and a line of best fit for the data set below. Label the axes and include a title. Book Price Price ($CAD) ($US) The Far Side Joy of Cooking Chicken Soup The Bike Book Hoyles Rules 9 7 Field Guide Romeo and Juliet 5 4 b) Describe the trend c) Describe the correlation d) Describe the relationship e) Use your line of best fit (LOBF) to determine the price of a US book if it costs $24 CAD f) Is your answer to e) interpolation or extrapolation? g) Use your LOBF to determine the price of a Canadian book if it costs $2 US. h) Is your answer to g) interpolation or extrapolation? 3) Sketch a scatter plot that could model each of the scenarios. Include a line of best fit with your scatter plot. Don t forget to label the axes. a) There is a strong positive correlation between a person s height and the length of their arm span. b) Studies show there is a moderate negative correlation between the number of times a student is late to class and marks achieved. Page 9 of 13

10 Curve of Best Fit Goal: Infer information from a scatter plot using a curve of best fit Not always does it make sense to draw a line of best fit! Sometimes when you follow the trend of the data you will not be able to draw a single straight line. Example 1 A weather forecaster measures and plots the temperature every 2 hours on a summer day. The points do not lie on a straight line, but there is still a relationship between the time of day and the temperature outside. Therefore instead of drawing a LOBF we can draw a To draw a COBF, draw a smooth curve that passes through as many point as possible. We can still use the COBF to make predictions about the data. 1) Between what times did the greatest (highest) temperature occur? 2) What is the temperature at 5:00 am? Example 2 Draw a curve of best fit for each set of data and describe any trends in the data. Page 10 of 13

11 Example 3 A soccer ball is kicked up into the air from the ground. The height of the ball is measured at regular time intervals. The data is as follows: Time (s) Height (m) a) Plot the points in the table above. Remember to include ALL the proper labels. b) What trend do you see in the data? Explain the trend. c) Draw the curve of best fit on your graph. d) When (at what time) do you think the ball is at its greatest height? Use the graph to find your answer and show your proof of the answer on the graph. e) When is the ball at a height of 5 m? How do you know this? f) When does the ball hit the ground? How do you know this when you look at your graph? Page 11 of 13

12 Curve of Best Fit Worksheet Problem #1 An Internet host is a computer directly connected to the Internet. The number of Internet Hosts around the world has grown quickly. The data in the table are for January of each given year. Year Internet Hosts (millions) a) Graph the data and draw a curve of best fit. Remember to include ALL the proper labels. b) What trend do you see in the graph/data? Explain the trend. c) Use your COBF to estimate the number of Internet hosts in d) When might the number of Internet hosts reach 500 million? Justify your answer. Problem #2 Page 12 of 13

13 The high divers at Canada s Wonderland perform competitive dives from a height of 21 m. A diver s height is measured every 0.2 s. The data is recorded in the table below. Time (s) Height (m) a) Graph the data and draw a curve of best fit. Remember to include ALL the proper labels. b) What trend do you see in the graph/data? Explain the trend. c) Use your COBF to estimate when the diver will be 10 m above the water. d) When does the diver reach the water? How do you know?. Page 13 of 13