Scatter Graphs Correlation Objectives To draw a Scatter

Scatter Graphs & Correlation Objectives To draw a Scatter Graph To describe any Correlation To use a Line of Best Fit to make predictions

Scatter Graphs Hours of sunshine Scatter graphs are used to show whethere is a relationship between two sets of data. Temperature (o. C)

Scatter Graphs The relationship between the data can be described as either: 1. A positive correlation. As one quantity increases so does the other. 2. A negative correlation. As one quantity increases the other decreases. Weight Positive Correlation Shoe Size Height Car Value 3. No correlation. Both quantities vary with no clear relationship. Age of Car Negative correlation Annual Income No correlation

A positive or negative correlation is represented by a straight line with a positive/negative gradient. The strength of the correlation depends on the spread of points around the imagined line. Strong Positive Weak Positive Strong negative Weak negative

Negative Outside air temperature KS 3 Results 5 Positive Daily hours of sunshine Value of car (£) Negative None Car engine size (cc) Sales of Sun cream 4 3 Height (mpg) 2 Petrol consumption Positive Maths test scores Heating bill (£) 1 Physics test scores State the type of correlation for the scatter graphs below. 6 Negative Age of car (years)

(1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and describe the correlation. Size 5 12 7 10 10 9 8 11 6 8 Mass 65 97 68 92 78 78 76 88 74 80 Mass (kg) 100 95 90 85 80 75 70 65 60 4 5 6 7 8 9 10 11 12 13 Shoe Size Question 1

(1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and describe the correlation. Size 5 12 7 10 10 9 8 11 6 8 Mass 65 97 68 92 78 78 76 88 74 80 Mass (kg) 100 95 90 85 80 75 70 65 60 4 5 6 7 8 9 10 11 12 13 Shoe Size

(1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and describe the correlation. Size 5 12 7 10 10 9 8 11 6 8 Mass 65 97 68 92 78 78 76 88 74 80 Mass (kg) 100 95 90 85 80 75 70 65 60 4 5 6 7 8 9 10 11 12 13 Shoe Size

(1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and describe the correlation. Size 5 12 7 10 10 9 8 11 6 8 Mass 65 97 68 92 78 78 76 88 74 80 Mass (kg) 100 95 90 85 80 75 70 65 60 4 5 6 7 8 9 10 11 12 13 Shoe Size

(1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and describe the correlation. Size 5 12 7 10 10 9 8 11 6 8 Mass 65 97 68 92 78 78 76 88 74 80 Mass (kg) 100 95 90 85 80 75 70 65 60 4 5 6 7 8 9 10 11 12 13 Shoe Size

(1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and describe the correlation. Size 5 12 7 10 10 9 8 11 6 8 Mass 65 97 68 92 78 78 76 88 74 80 Mass (kg) 100 95 90 85 80 75 70 65 60 4 5 6 7 8 9 10 11 12 13 Shoe Size

(1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and describe the correlation. Size 5 12 7 10 10 9 8 11 6 8 Mass 65 97 68 92 78 78 76 88 74 80 Mass (kg) 100 95 90 85 80 75 70 65 60 4 5 6 7 8 9 10 11 12 13 Shoe Size

(1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and describe the correlation. Size 5 12 7 10 10 9 8 11 6 8 Mass 65 97 68 92 78 78 76 88 74 80 Mass (kg) 100 95 90 85 80 75 70 65 60 4 5 6 7 8 9 10 11 12 13 Shoe Size

(1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and describe the correlation. Size 5 12 7 10 10 9 8 11 6 8 Mass 65 97 68 92 78 78 76 88 74 80 Mass (kg) 100 95 90 85 80 75 70 65 60 4 5 6 7 8 9 10 11 12 13 Shoe Size

(1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and describe the correlation. Size 5 12 7 10 10 9 8 11 6 8 Mass 65 97 68 92 78 78 76 88 74 80 Mass (kg) 100 95 90 85 80 Positive Correlation 75 70 65 60 4 5 6 7 8 9 10 11 12 13 Shoe Size

(2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and describe the correlation. 6 0. 5 8 3 8 10 Visitors 300 475 100 390 200 100 Number of Visitors Hours Sunshine 7 5 3 2 175 220 350 320 500 450 400 350 300 250 200 150 100 0 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine Question 2

(2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and describe the correlation. 6 0. 5 8 3 8 10 Visitors 300 475 100 390 200 100 Number of Visitors Hours Sunshine 500 450 400 350 300 250 200 150 100 0 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 7 5 3 2 175 220 350 320

(2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and describe the correlation. 6 0. 5 8 3 8 10 Visitors 300 475 100 390 200 100 Number of Visitors Hours Sunshine 500 450 400 350 300 250 200 150 100 0 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 7 5 3 2 175 220 350 320

(2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and describe the correlation. 6 0. 5 8 3 8 10 Visitors 300 475 100 390 200 100 Number of Visitors Hours Sunshine 500 450 400 350 300 250 200 150 100 0 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 7 5 3 2 175 220 350 320

(2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and describe the correlation. 6 0. 5 8 3 8 10 Visitors 300 475 100 390 200 100 Number of Visitors Hours Sunshine 500 450 400 350 300 250 200 150 100 0 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 7 5 3 2 175 220 350 320

(2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and describe the correlation. 6 0. 5 8 3 8 10 Visitors 300 475 100 390 200 100 Number of Visitors Hours Sunshine 500 450 400 350 300 250 200 150 100 0 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 7 5 3 2 175 220 350 320

(2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and describe the correlation. 6 0. 5 8 3 8 10 Visitors 300 475 100 390 200 100 Number of Visitors Hours Sunshine 500 450 400 350 300 250 200 150 100 0 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 7 5 3 2 175 220 350 320

(2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and describe the correlation. 6 0. 5 8 3 8 10 Visitors 300 475 100 390 200 100 Number of Visitors Hours Sunshine 500 450 400 350 300 250 200 150 100 0 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 7 5 3 2 175 220 350 320

(2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and describe the correlation. 6 0. 5 8 3 8 10 Visitors 300 475 100 390 200 100 Number of Visitors Hours Sunshine 500 450 400 350 300 250 200 150 100 0 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 7 5 3 2 175 220 350 320

(2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and describe the correlation. 6 0. 5 8 3 8 10 Visitors 300 475 100 390 200 100 Number of Visitors Hours Sunshine 7 5 3 175 220 350 320 500 450 Negative 400 350 300 250 Correlation 200 150 100 0 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 2

Drawing a Line of Best Fit A line of best fit can be drawn to data that shows a correlation. The stronger the correlation between the data, the easier it is to draw the line. The line can be drawn by eye and should have roughly the same number of data points on either side. Lobf Note: Your line does NOT have to start at the origin (0, 0)

(1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and describe the correlation. Size 5 12 7 10 10 9 8 11 6 8 Mass 65 97 68 92 78 78 76 88 74 80 Mass (kg) 100 95 90 85 80 (b) Draw a line of best fit and comment on the correlation. Positive 87 kg (c) Use your line of best fit to estimate: 75 70 65 (i) Size 6 60 4 5 6 7 8 9 10 11 12 13 Shoe Size The mass of a man with shoe size 10½. (ii) The shoe size of a man with a mass of 69 kg.

(2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and describe the correlation. 6 0. 5 8 3 8 10 Visitors 300 475 100 390 200 100 Number of Visitors Hours Sunshine 500 450 5 3 2 175 220 350 320 (b) Draw a line of best fit and comment on the correlation. Negative 400 350 300 250 7 (c) Use your line of best fit to estimate: 310 (i) 200 150 5½ 100 0 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine The number of visitors for 4 hours of sunshine. (ii) The hours of sunshine when 250 people visit.

Size 5 12 7 10 10 9 8 11 6 8 Mass 65 97 68 92 78 78 76 88 74 80 Mass (kg) 100 95 90 85 80 75 70 65 60 4 5 6 7 8 9 10 11 12 13 Shoe Size

1. The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and describe the correlation. Size 5 12 7 10 10 9 8 11 6 8 Mass 65 97 68 92 78 78 76 88 74 80 Mass (kg) 100 95 90 85 80 75 70 65 60 4 5 6 7 8 9 10 11 12 13 Shoe Size Worksheet 1

2. The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and describe the correlation. 6 0. 5 8 3 8 10 Visitors 300 475 100 390 200 100 Number of Visitors Hours Sunshine 7 5 3 2 175 220 350 320 500 450 400 350 300 250 200 150 100 0 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine Worksheet 2