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Investigation: Scatter plots and body measurements

Overview
Activity
Reflection

Investigate how to collect and analyze statistical data related to growth and health.

Objectives
  • To collect data.
  • To analyze and interpret data.
  • To consider correlation and relationships in data.
Materials
  • Tape measure
  • Graphing calculator or digital version (https://www.desmos.com/calculator)
  • Pen or pencil
  • Paper

Scatter plots and body measurements

Vocabulary
Define the following terms and use them throughout the activity:
  • Biometric data
  • Scatter plot
  • Positive correlation
  • Negative correlation
  • Strong correlation
  • Weak correlation
Biometric data
One way math can be used in our health is to measure dimensions of the body and limbs. Common body dimensions that are measured include: arm-span, height, hip height, and 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.
A person standing illustrating arm span measured as the length of a person's arm, fingertips to fingertips.
Arm span
Also known as reach, it is the measurement of the length of a person’s arms, fingertips to fingertips.
A person standing illustrating hip height measured between hip line and bottom of the feet.
Hip height
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 standing illustrating height measured top of the head and bottom of the feet.
Height
A person’s height is measured from the top of their head to the bottom of their feet, when standing.
3 footprints illustrating stride length measured between the heel of a person's footprint and the heel of the same footprint two steps on.
Stride length
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.
Interpreting measurements
One way of understanding these measurements is by plotting ordered pairs onto a scatter plot. This makes it easier to recognize patterns in the data, especially whether or not these patterns appear to be linear.
A scatter plot titled Linear Scatter with the y-axis ranging from 150 to 195 titled Height in centimeters and the x-axis ranging from 150 to 195 titled Arm span in centimeters. The graph shows points roughly sloping upward from the bottom left to the upper right of the graph.
Linear patterns reveal whether or not two measurements are connected to each other. For example, there is a linear relationship between a person’s height and arm span because, in general, as a person’s height increases so does their arm span.
A scatter plot titled No correlation with the y-axis ranging from 10 to 20 and the x-axis ranging from 65 to 85. The graph shows a random distribution of points.
If there is not a linear relationship between two pairs of data then the scatter plot shows a more random distribution. This is important to know because the presence of a linear pattern signals that the two sets of data correlate. However, it is equally important to note that correlation doesn't necessarily indicate a "causal link", but we'll look at this further on.
Procedure
  • Take measurements of the height of students in your class and the arm span of students in your class.
  • Using a digital tool, plot the obtained measurements against each other in a scatter plot.
Investigate
Consider the following questions once you have completed the above procedure.
1.
Comment on any relationships between the arm span and height and form predictions on the arm-span of a person based on their height.
2.
Discuss with a partner any relationships that you have identified and the types of correlations that lead you to make those conclusions.

Answer the questions below after you have completed the activity.

Discussion
1.
Come up with an example where a scatterplot might indicate a relationship, but there is not neccessarily a relationship between the two variables.

Outcomes

8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

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