13. Mathematics and health Cambridge University Press  G K Powers 2013 Study guide Chapter 13

Body measurements Scatterplot Body proportions do not change with age and are extremely important in art and medicine. Scatterplot A scatterplot is a graph of ordered pairs of numbers. Each ordered pair is a dot on the scatterplot HSC Hint – Scatterplots are used to determine if there is a relationship between two quantities. Cambridge University Press  G K Powers 2013

Interpreting scatterplots Look for a clear pattern. Linear relationships approximate a straight line. Non-linear relationships approximate a curve. HSC Hint – An outlier does not fit the pattern shown by the other points. Cambridge University Press  G K Powers 2013

Correlation coefficient Correlation coefficient (r) measures the strength of a linear relationship (−1≤ r ≤ 1) Positive correlation (0 to +1): both quantities increase and decrease at the same time. Zero or no correlation (0): no relationship between the quantities. Negative correlation (0 to −1): one quantity increases, the other quantity decreases. HSC Hint – A high correlation is not sufficient to imply causation. Cambridge University Press  G K Powers 2013

Line of best fit A line of best fit is a straight line that approximates a linear relationship between points. The equation of the line of best fit is found using the gradient-intercept formula: . HSC Hint – Draw a line of best fit that seems to balance out the points around the line. Cambridge University Press  G K Powers 2013

Method of least squares Method of least squares is a line of best fit that minimises the sum of the squares of the vertical distances (or residuals). Equation of least squares line of best fit uses these formulas: r − correlation coefficient sx and sy − standard deviation of x and y and − mean of x and y HSC Hint – Make sure you can use your calculator to determine the correlation coefficient. Cambridge University Press  G K Powers 2013

Medication Medication calculations are required related to the amount per dose, the frequency of dosage and the dosages for different medication types. Medications involve concentrations expressed as mass/volume such as 5 g/10 mL. A concentration is a measure of how much of a given substance is mixed with another substance. HSC Hint – Make sure the correct units are substituted into the above formulas for medication. Cambridge University Press  G K Powers 2013

Life expectancy Life expectancy is the number of years a person of a particular age today can expect to live. Factors affecting life expectancy include genetics', dietary behaviours, the effectiveness of healthcare systems and living conditions. Australia enjoys one of the highest life expectancies of any country in the world. HSC Hint – Life expectancy tables and graphs often contain a legend. Read the information in the legend before accessing the data. Cambridge University Press  G K Powers 2013

Predicting life expectancy Rate of growth of life expectancy over the century has not been constant. HSC Hint – A line of best fit is often used to predict life expectancy. Cambridge University Press  G K Powers 2013