Bivariate data data from two variables e.g. Maths test results and English test results. Interpolate estimate a value between two known values.
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1 Key words: Bivariate data data from two variables e.g. Maths test results and English test results Interpolate estimate a value between two known values. Extrapolate find a value by following a pattern and going outside the range of known values. This not reliable because the pattern may not continue outside the existing values Lines of best fit - a line that goes roughly through the middle of all the scatter points on a graph. Correlation a measurement of how strongly connected two sets of data are Types of Correlation: y-axis y-axis y-axis x-axis x-axis Positive correlation Negative correlation No correlation x-axis Strong correlation the points lie close to the line of best fit Weak correlation the points are spread out from the line of best fit but still follow the trend Causation two variables which are linked and a change in one variable causes a change in the other variable e.g. number of ice-cream sales and the temperature Outlier - A value that is much smaller or larger than most of the other values in a set of data Page 1 of 14
2 History Test Score Vlaue of car Number of pets Temperature Scatter Graph Type of Correlation Describe Ice creams sold House Number Age of Car Geogrpahy Test score Page 2 of 14
3 Car Value 1. The scatter graph shows the change in car values over time Age in years a. Give the co-ordinates of the outlier b. What type of correlation is this? c. Describe the relationship between the two variables d. Using a line of best fit, i. What would be the approximate value of the car after 4 ½ years? ii. What would be the approximate value of the car after 6 years? iii. Why is this not a reliable value? Give a reason for your answer Page 3 of 14
4 Number of plums 2. The scatter graph shows the heights of 7 plum trees and the number of plums on each Height of tree (m) a. Describe the relationship between the number of plums on a tree and the height of the tree 3 more trees were measured and the details entered on the table below. Height (m) Number of plums b. Plot these values on the scatter graph. There is an outlier c. Write down the coordinates of this outlier d. Draw a line of best fit ignoring the outlier e. Estimate the number of plums on a tree 2.4m tall f. What percentage of trees have more than 15 plums on them? Page 4 of 14
5 3. The table show the results for a Year 10 Maths and English test Maths English a. Draw a scatter graph for this data. b. What type of correlation is shown? c. Using a line of best fit, i. estimate Verity s English score if her Maths score is 36 ii. Nick scored 49 in his English test, estimate his Maths score. d. Which of these two estimates is less reliable? Why? Page 5 of 14
6 4. The table shows the height of a tomato plant (cm) and the number of days since it was planted Number of days Height (cm) a. Plot this data on the graph below, remembering to label your axes b. How could this scatter graph be improved? c. Comment on the relationship between the height of the tomato plants and the number of days since they were planted d. Estimate the height of the tomato plant exactly eight weeks after planting e. Why would it not be sensible to use the line of best fit to estimate the height after three months? f. What is the percentage change in height between days 40 and 70? Page 6 of 14
7 5. The table shows the height of a person and the number of ice-creams they eat in the summer. Height (m) Number of ice creams a. What type of correlation would you expect if you plotted this scatter graph? b. Explain why? 6. The table shows a person s house number and their height in metres. House Number Height (m) Why is a scatter graph not an appropriate diagram for this data? Page 7 of 14
8 History Test Score Vlaue of car Number of pets Temperature Answers Scatter Graph Type of Correlation Describe the relationship Strong positive correlation The number of ice creams sold increases with the temperature Ice creams sold House Number No correlation The is no correlation between a person s house number and the number of pets that they own Strong negative Correlation As a car gets older it s value decreases Age of Car Geogrpahy Test score Weak positive correlation There is some correlation between a student s geography test scores and history scores. As the geography score increases, the history score increases too Page 8 of 14
9 Car Value 1. The scatter graph shows the change in car values over time Age in years e. Give the co-ordinates of the outlier - (3, 1000) f. What type of correlation is this? strong negative correlation g. Describe the relationship between the two variables - As a car gets older the value decreases h. Using a line of best fit, iv. What would be the approximate value of the car after 4 ½ years? 2800 v. What would be the approximate value of the car after 6 years? 600 vi. Why is this not a reliable value? Give a reason for your answer beyond the data given/ Car could be a vintage car Page 9 of 14
10 Number of plums 2. The scatter graph shows the heights of 7 plum trees and the number of plums on each Height of tree (m) a. Describe the relationship between the number of plums on a tree and the height of the tree. As the height of the tree increases, the number of plums also increases 3 more trees were measured and the details entered on the table below. Height (m) Number of plums b. Plot these values on the scatter graph. There is an outlier c. Write down the coordinates of this outlier (1,21) d. Draw a line of best fit ignoring the outlier e. Estimate the number of plums on a tree 2.4m tall 23 plums f. What percentage of trees have more than 15 plums on them? 60% Page 10 of 14
11 English 3. The table show the results for a Year 10 Maths and English test Maths English a. Draw a scatter graph for this data Maths b. What type of correlation is shown? Positive correlation c. Using a line of best fit, a. estimate Verity s English score if her Maths score is b. Nick scored 49 in his English test, estimate his Maths score d. Which of these two estimates is less reliable? Why? Nick s score is less reliable as the data is outside the given range Page 11 of 14
12 height cm 4. The table shows the height of a tomato plant (cm) and the number of days since it was planted Number of days Height (cm) a. Plot this data on the graph below, remembering to label your axes Number of days b. How could this scatter graph be improved? Change the axes scale/not start at 0 c. Comment on the relationship between the height of the tomato plants and the number of days since they were planted The height of the tomato plants increases with the number of days d. Estimate the height of the tomato plant exactly eight weeks after planting (56 days) 12.6cm e. Why would it not be sensible to use the line of best fit to estimate the height after three months? Outside the data range given f. What is the percentage change in height between days 40 and 70? Approx. 58% Page 12 of 14
13 5. The table shows the height of a person and the number of ice-creams they eat in the summer. Height (m) Number of ice creams a. What type of correlation would you expect if you plotted this scatter graph? No correlation b. Explain why? There is no relationship between a person s height and the number of ice-creams they eat 6. The table shows a person s house number and their height in metres. House Number Height (m) Why is a scatter graph not an appropriate diagram for this data? There is no relationship between a person s house number and their height Page 13 of 14
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