Processing and Representing Data 11 May 2019 Processing and Representing Data Scatter Graphs
Learning Objectives draw a scatter diagram, plotting points from a table understand correlation and distinguish between positive, negative and zero correlation using the diagram and line of best fit understand and describe the relationship between two variables draw a line of best fit both by eye and using the mean point find the equation of the line of best fit and use it to predict values Grade D/C Textbook Reference section 4.4 page 102 section 4.5 page 103 Section 4.6 page 106 Section 4.7 page 108 Further Practise 10 Ticks level 7 pack 1 page 31 - 34 Mep book 13 section 7
Key ideas: A scatter graph enables you to see if there is a linear relationship between two variables, e.g. height and arm span A relationship between pairs of variables is called correlation A line of best fit is a straight line drawn to represent the trend of the data so that the plotted points are evenly scattered either side of the line The line of best fit can be used to estimate a missing variable when the corresponding data is known An outlier is a point that doesn’t fit with the general trend of the data An exam question may ask for a description of the correlation or the relationship between the variables these are different questions don’t mess it up!
Correlation looks like this – page 104 Need to add negative correlation
(1). The table below shows the shoe size and mass of 10 men. 4 5 6 7 8 9 10 11 12 13 Shoe Size 60 65 70 75 80 85 90 95 100 Mass (kg) (1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and draw a line of best fit. 74 88 76 78 92 68 97 Mass Size (b) Draw a line of best fit and comment on the correlation. Positive 87 kg (c) Comment on the relationship between shoe size and mass. (d) Use your line of best fit to estimate: The mass of a man with shoe size 10½. (ii) The shoe size of a man with a mass of 69 kg. Size 6
(a) Plot a scatter graph for this data and draw a line of best fit. 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors (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 draw a line of best fit. 320 220 175 50 390 475 Visitors 0.5 Hours Sunshine (b) Draw a line of best fit and comment on the correlation. Negative (c) comment on the relationship between the number of visitors and the hours of sunshine. 310 5 ½ (d) Use your line of best fit to estimate: The number of visitors for 4 hours of sunshine. (ii) The hours of sunshine when 250 people visit.
Your Turn Exercise 4D page 105 Exercise 4E page 107 Exercise 4F page 110
GCSE Statistics Extension 5.3 Causal Relationships page 175 5.4 Line of best fit plot it through the mean for each data set 5.6 Finding the equation of the line of best fit 5.7 Fitting a line of best fit to a non-linear model of the form y = axn + b and y = kax 5.8 Spearman’s rank correlation coefficient 5.9 Interpretation of Spearman’s correlation coefficient