1. Mathematics and Health Body Measurements Medication Life Expectancy
Focus Study
Mathematics and Health
Body Measurements
Medication
Life Expectancy

2. Basic Concepts Investigate and plot data on body measurements
Draw lines of ‘best fit’
Calculate and use correlation coefficients
Use units of mass smaller than the gram
Convert measurements and concentrations of medicine
Calculate dosage rates and strengths
Interpret and plot life expectancy data
Use and construct scatterplots
Make predictions from data

3. Scatter Plots
There are rules relating our body proportions. For example, the ratio of height to arm span is and the average person is 7.5 heads tall. Body proportions do change with age and are extremely important in art and medicine. A scatter plot is a way to determine if there is a relationship between two numerical variables.
Height in cm
Armspan in cm
For a random selection of our class, we will measure height and arm span and plot them on the grid.

4. Ratios in the human body
There are many examples of consistent ratios in the human body…the closer to the ‘golden ratio’ somebody’s features are, the more attractive they are generally felt to be.

5. Interpreting Scatter Plots
The three scatterplots drawn below show clear but different patterns
for each set of points. If the points seem to approximate a straight
line, the relationship is linear. On the other hand, if the points
approximate a curve the relationship is non-linear. A positive linear pattern has a positive slope and a negative linear pattern has a negative slope.
The scatterplot shown on the right has a positive linear pattern and contains an outlier. An outlier is data that appears to stand out from the main body of the data set. It does not fit the pattern shown by the other points and cannot be described by the relationship between the two variables.

8. Step it up…

10. Line of Best Fit
If a pair of variables appears to be related, as indicated by a linear pattern of dots on a scatterplot, then we can draw a straight line that fits the points plotted and use this line to predict the value of one variable given the value of the other. This line is known as the:
• ‘line of best fit’ or
• ‘line of good fit’ or
• ‘regression line’ or
• ‘trendline’ or
• ‘least-squares line of best fit’.

13. Drawing a Line of Best Fit
The line must have about the same number of dots above and below it. The line need not pass through any of the points but must balance the points above and below.

17. Correlation Coefficient
The strength of a linear relationship is an indication of how closely the points in the scatterplot fit a straight line. If the points in the scatterplot lie exactly on a straight line, we say there is a perfect linear relationship. If there is no fit at all we say there is no relationship. To measure the strength of a linear relationship we use a correlation coefficient (r), which has the following properties:

21. Least-squares Line of best Fit
The simplest method of finding the equation of the least-squares line of best fit is to use a spreadsheet.
To find the least-squares line of best fit equation from a table of values comparing variables x and y, we need to calculate r, the mean and standard deviation of the x scores, and the mean and standard deviation of the y scores.

26. Measurement Calculations
The most common forms of a drug are tablets and liquids. As the amount of active drug taken (the dosage) is usually small, it is measured in milligrams mg. (1000 mg is equal to 1 g.)

28. Using rates in dosages Medicine for nursing
A patient is prescribed 400 mg of a painkiller. The medication available contains 80 mg in 10 mL. How much medication should be given to the patient?
Medicine for nursing

31. Fried’s Formula

32. Young’s formula

33. Clark’s formula

34. Drip Rates and Flow Rates
A patient is to receive 1.6 L of fluid over 10 h. What is the flow rate in mL/h?

35. Drips and Drops…
A patient is to receive 1.2 L of fluid over 4 h through an IV drip. There are 15 drops/mL. How many drops per minute are required?