# PH.2 a-d - Data Analysis

The student will investigate and understand how to analyze and interpret data. Key concepts include

a)  description of a physical problem is translated into a mathematical statement in order to find a solution;

b)  relationships between physical quantities are determined using the shape of a curve passing through experimentally obtained data;

c)  the slope of a linear relationship is calculated and includes appropriate units; and

d)  interpolated, extrapolated, and analyzed trends are used to make predictions.

Bloom's Levels:  Analyze; Understand

### BIG IDEAS

• I can determine how steep a roof must be so that snow is able to slide off.
• I can determine the impact a steep hill has on the average and instantaneous speed of a runner.
• I can determine how much money I will need to buy any quantity of an item.
• I can compare my results to others' to determine a reasonable conclusion.

### UNDERSTANDING THE STANDARD

The concepts developed in this standard include the following:
• Mathematics is a tool used to model and describe phenomena.
• Graphing and dimensional analysis are used to reveal relationships and other important features of data.
• Predictions are made from trends based on the data.
• The shape of the curve fit to experimentally obtained data is used to determine the relationship of the plotted quantities.
• All experimental data do not follow a linear relationship.
• The area under the curve of experimentally obtained data is used to determine related physical quantities.
• Not all quantities add arithmetically. Some must be combined using trigonometry. These quantities are known as vectors.
• Physical phenomena or events can often be described in mathematical terms (as an equation or inequality).

### ESSENTIALS

In order to meet this standard, it is expected that students will

a-b) recognize linear and nonlinear relationships from graphed data.

where appropriate, draw a straight line through a set of experimental data points and determine the slope and/or area under the curve.

c) use dimensional analysis to verify appropriate units.

d-e) combine vectors into resultants utilizing trigonometric or graphical methods.

resolve vectors into components utilizing trigonometric or graphical methods.

### KEY VOCABULARY

Updated: Dec 01, 2017