Scatter Graphs
The following table is a record of average monthly rainfall and average monthly temperature. Rainfall (mm) 60 45 40 30 20 11 10 25 38 50 62 Temp. (C) 12 15 16 32 28 22 10 20 30 40 50 60 5 15 25 • • • • • Temp. • • • • • • • Rainfall
• * The line cuts the y-axis at 32 Gradient = -15/50 = -3/10 20 30 40 50 60 5 15 25 Rainfall Temp. • The line cuts the y-axis at 32 Pick another point where line passes through a junction.*(50, 15) Gradient = -15/50 = -3/10 T = -3/10 R + 32 * We will now draw a line of best fit and find its equation 1. Estimate the rainfall when the temperature is 20C. Approx 38mm 2. Estimate the temperature when the rainfall is 50mm. Approx. 15C
When the line of best fit slopes downwards from left to right, then there is a negative correlation. When the line of best fit slopes upwards from left to right, then there is a positive correlation.
• • • • • • • • • • • • • • * y = mx + c y = mx + 2 Physics mark 5 10 15 20 30 • • • • • • • • y = mx + c y = mx + 2 10 * Physics mark 9 y = x + 2 9 10 • • • • • Maths mark
Example 1:- The diagram on the next slide shows the marks obtained in both Physics and Maths exams by a number of pupils. Can you make a general statement about the marks? On the diagram draw the line which best fits the data. Use this line to estimate the following:- a) The mark for a pupil who missed his Maths exam but scored 72 in his Physics exam. b) The mark for a pupil who missed his Physics exam but scored 40 in his Maths exam.
Can you make a general statement about the marks? On the diagram draw the line which in your opinion best fits the data. Use this line to estimate the following:- a) The mark for a pupil who missed his Maths exam but scored 38 in his Music exam. b) The mark for a pupil who missed his Music exam but scored 28 in his Maths exam.
Example 2. The diagram shows the marks obtained by a number of pupils in both Maths and Music exams.
Example 3. The diagram shows the amount of damage caused by fires in houses (thousands of £s) and the corresponding response time by the Fire Brigade(minutes) in getting to that particular fire. Can you make a general statement about the graph? y = mx + c 3 * 5 *
On the diagram draw the line which, in your opinion, best fits the data. Use this line to estimate the following:- The expected cost of the damage for a house if it takes the Fire Brigade 10 minutes to get to the fire? b) The expected response time if it is hoped that damage could be kept below £2000.
Example 4. The height h(cm) and the weight w(kg) of a number of pupils were measured. The results are shown in the scatter diagram. What can you say in general about the graph?
Use this line to estimate the following:- On the diagram draw the line which, in your opinion, best fits the data. Use this line to estimate the following:- a) The weight of a boy whose height is 165cm. b) The height of a pupil with a weight of 64kg.
Example 5. Tests were carried out on cars to find the length of the skid mark left after cars braked.
The scatter graph shows the results obtained in the trials. After an accident the skid mark was estimated to be 64cm. a) What does this tell you about the cars speed? b) What length of skid mark might be left by a car traveling at 95 km/hr.