1. Processing and Representing Data
11 May 2019
Processing and Representing Data
Scatter Graphs

2. 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
Mep book 13 section 7

3. 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!

4. Correlation looks like this – page 104
Need to add negative correlation

5. (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

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.

7. Your Turn
Exercise 4D page 105
Exercise 4E page 107
Exercise 4F page 110

8. 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