8. Two Variable Data Analysis

Ontario Grade 9 (MTH1W) 2021 Edition

Investigation: Scatterplots and body measurements

Lesson

One way that Mathematics can be used to benefit our health is to measure dimensions of the body and limbs. Common body dimensions that are measured include:

- arm-span
- height
- hip height
- stride length

Once we understand these measurements, we can look at why these measurements can be important and how these measurements relate to each other and to other major factors like age and gender.

Also known as reach, it is the measurement of the length of a person’s arms, fingertips to fingertips.

Is measured as the distance between your hip line and the bottom of your feet. The hip line is located at the widest part of a person’s hips.

A person’s height is measured from the top of their head to the bottom of their feet, when standing.

The measurement of a person's natural pace, it is the distance between the heel of a person’s footprint and the heel of the same footprint two steps on.

Information about these measurements is published by various sources, such as the Australian Bureau of Statistics (ABS) and medical publications.

- A tape measure or similar instrument
- A digital tool that can be used to create scatterplots, such as Excel

- Measure the height of each student in your class
- Measure the arm span of each student in your class
- Plot the measurements against each other in a scatterplot

- How would you describe the correlation of these two variables?
- If there is a correlation, which variable do you think is the independent variable and which is the dependent variable?

Create a scatter plot to represent the relationship between two variables, determine the correlation between these variables by testing different regression models using technology, and use a model to make predictions when appropriate.

Describe the value of mathematical modelling and how it is used in real life to inform decisions.