Tuesday October 24 First Math Contest of the year room am,

Transcription

1 Tuesday October 24 First Math Contest of the year room am, Then every second last Tuesday of the month. 1

2 MPM 1DI U4 D3 Line of Best Fit A line of best fit (or "trend" line) is a straight line that best represents the data on a scatter plot. This line may pass through some of the points, none of the points, or all of the points. You can examine lines of best fit with: 1. paper and pencil only, 2. a combination of technology and paper and pencil, 3. or solely with technology Example: Is there a relationship between the fat grams and the total calories in fast food? Sandwich Total Fat (g) Total Calories Hamburger Cheeseburger Quarter Pounder Quarter Pounder 30 with Cheese 530 Big Mac Arch Sandwich Special Arch Special with Bacon Crispy Chicken Fish Fillet Grilled Chicken Grilled Chicken 5 Light Describe the trend of the data. As the fat content increases the caloric content increases. Since both values are increasing this is a positive correlation. It is also Linear since the plotted points nearly form a line. 2

3 The LINE OF BEST FIT: allows us to make predictions for values not actually recorded and plotted. INTERPOLATION: involves making a prediction of a value WITHIN the recorded data. EXTRAPOLATION: involves making a prediction of a value OUTSIDE the recorded data. Use your line of best fit to make the following predictions: How many grams of fat would be in an item with 400 calories? Did you interpolate or extrapolate? There would be approximately 17.5g of fat. This is interpolation because it is inside the range of data already gathered. How many calories would be in an item with 650 calories? Did you have to extend your line of best fit? Did you use interpolation or extrapolation? There would be approx. 705 calories. This is extrapolation because it is outside the range of data. Are your answers the same as your neighbours? If not who has the correct answer? 3

4 Your answer will be considered CORRECT, as long as your coordinates are correct for your line of best fit. So, if each answer may be slightly different, which answer is the REAL "line of best fit? To answer this question, we need the assistance of technology. Simply stated, the technology has the capability of determining which line will "actually" represent the REAL line of best fit. Example 2: The following table represents data from a survey to determine the relationship between a student s age and the number of novels they have read in the past year. Age # of novels read 1. Identify the independent and dependent variables Plot the data in a spreadsheet 3. Identify the trend. 4. Draw a line of best fit. (you will find the trendline under Series) 5. Identify any outliers. 6. Predict how many novels a 20 year old may read in one year. 4

5 Key Concepts 1. A pattern in the graph of a set of data often indicates a trend. If it approximates a linear pattern a line of best fit can be drawn. 2. You can interpolate values between those in a set of data. Practice eye balling the correct line of best fit Pgs # 2 4, 7 5