An ecologist is studying the effect of soil salinity, s s\,s mS/cm, on the maximum growth height, h h\,h cm, of a marsh grass. She records s s\,s and h h\,h at each of 10 sites and plots the data on a scatter diagram.
For 9 of the sites the points show a strong negative linear correlation, and the product moment correlation coefficient for those 9 sites is -0.826.
The 10th site, Site Omega, is plotted at (48, 82)(48,\ 82)(48, 82), which lies well above the trend shown by the other 9 sites.
In this question you must show detailed reasoning.
State why Site Omega might be considered an outlier in this context.
State, giving a reason, what effect including Site Omega would have on the value of the product moment correlation coefficient.
The ecologist concludes that greater soil salinity causes the maximum growth height of the grass to decrease. Explain why the data do not justify this conclusion.
121 exam-style questions on OCR A Level Maths 2.2 Data Presentation and Interpretation, covering 2.2.1 Tables and diagrams for single variable data, 2.2.2 Area in a histogram, 2.2.3 Scatter diagrams and regression lines, 2.2.4 Informal interpretation of correlation, 2.2.5 Correlation and causation, 2.2.6 Measures of average and spread, 2.2.7 Calculations of mean and standard deviation, 2.2.8 Outliers, 2.2.9 Selecting or critiquing data presentation, and 2.2.10 Cleaning data. Each one has a worked solution and a mark scheme showing where the marks go.